Daily Papers

Graph convolutional networks (GCN) is widely used to handle irregular data since it updates node features by using the structure information of graph. With the help of iterated GCN, high-order information can be obtained to further enhance the representation of nodes. However, how to apply GCN to structured data (such as pictures) has not been deeply studied. In this paper, we explore the application of graph attention networks (GAT) in image feature extraction. First of all, we propose a novel graph generation algorithm to convert images into graphs through matrix transformation. It is one magnitude faster than the algorithm based on K Nearest Neighbors (KNN). Then, GAT is used on the generated graph to update the node features. Thus, a more robust representation is obtained. These two steps are combined into a module called pixel-wise graph attention module (PGA). Since the graph obtained by our graph generation algorithm can still be transformed into a picture after processing, PGA can be well combined with CNN. Based on these two modules, we consulted the ResNet and design a pixel-wise graph attention network (PGANet). The PGANet is applied to the task of person re-identification in the datasets Market1501, DukeMTMC-reID and Occluded-DukeMTMC (outperforms state-of-the-art by 0.8\%, 1.1\% and 11\% respectively, in mAP scores). Experiment results show that it achieves the state-of-the-art performance. https://github.com/wenyu1009/PGANet{The code is available here}.

The growing importance of data visualization in business intelligence and data science emphasizes the need for tools that can efficiently generate meaningful visualizations from large datasets. Existing tools fall into two main categories: human-powered tools (e.g., Tableau and PowerBI), which require intensive expert involvement, and AI-powered automated tools (e.g., Draco and Table2Charts), which often fall short of guessing specific user needs. In this paper, we aim to achieve the best of both worlds. Our key idea is to initially auto-generate a set of high-quality visualizations to minimize manual effort, then refine this process iteratively with user feedback to more closely align with their needs. To this end, we present HAIChart, a reinforcement learning-based framework designed to iteratively recommend good visualizations for a given dataset by incorporating user feedback. Specifically, we propose a Monte Carlo Graph Search-based visualization generation algorithm paired with a composite reward function to efficiently explore the visualization space and automatically generate good visualizations. We devise a visualization hints mechanism to actively incorporate user feedback, thus progressively refining the visualization generation module. We further prove that the top-k visualization hints selection problem is NP-hard and design an efficient algorithm. We conduct both quantitative evaluations and user studies, showing that HAIChart significantly outperforms state-of-the-art human-powered tools (21% better at Recall and 1.8 times faster) and AI-powered automatic tools (25.1% and 14.9% better in terms of Hit@3 and R10@30, respectively).

Retrieval-Augmented Generation (RAG) plays a crucial role in grounding Large Language Models by leveraging external knowledge, whereas the effectiveness is often compromised by the retrieval of contextually flawed or incomplete information. To address this, knowledge graph-based RAG methods have evolved towards hierarchical structures, organizing knowledge into multi-level summaries. However, these approaches still suffer from two critical, unaddressed challenges: high-level conceptual summaries exist as disconnected ``semantic islands'', lacking the explicit relations needed for cross-community reasoning; and the retrieval process itself remains structurally unaware, often degenerating into an inefficient flat search that fails to exploit the graph's rich topology. To overcome these limitations, we introduce LeanRAG, a framework that features a deeply collaborative design combining knowledge aggregation and retrieval strategies. LeanRAG first employs a novel semantic aggregation algorithm that forms entity clusters and constructs new explicit relations among aggregation-level summaries, creating a fully navigable semantic network. Then, a bottom-up, structure-guided retrieval strategy anchors queries to the most relevant fine-grained entities and then systematically traverses the graph's semantic pathways to gather concise yet contextually comprehensive evidence sets. The LeanRAG can mitigate the substantial overhead associated with path retrieval on graphs and minimizes redundant information retrieval. Extensive experiments on four challenging QA benchmarks with different domains demonstrate that LeanRAG significantly outperforming existing methods in response quality while reducing 46\% retrieval redundancy. Code is available at: https://github.com/RaZzzyz/LeanRAG

Large language models (LLMs) have demonstrated remarkable capabilities in a wide range of tasks, yet their application to specialized domains remains challenging due to the need for deep expertise. Retrieval-augmented generation (RAG) has emerged as a promising solution to customize LLMs for professional fields by seamlessly integrating external knowledge bases, enabling real-time access to domain-specific expertise during inference. Despite its potential, traditional RAG systems, based on flat text retrieval, face three critical challenges: (i) complex query understanding in professional contexts, (ii) difficulties in knowledge integration across distributed sources, and (iii) system efficiency bottlenecks at scale. This survey presents a systematic analysis of Graph-based Retrieval-Augmented Generation (GraphRAG), a new paradigm that revolutionizes domain-specific LLM applications. GraphRAG addresses traditional RAG limitations through three key innovations: (i) graph-structured knowledge representation that explicitly captures entity relationships and domain hierarchies, (ii) efficient graph-based retrieval techniques that enable context-preserving knowledge retrieval with multihop reasoning ability, and (iii) structure-aware knowledge integration algorithms that leverage retrieved knowledge for accurate and logical coherent generation of LLMs. In this survey, we systematically analyze the technical foundations of GraphRAG and examine current implementations across various professional domains, identifying key technical challenges and promising research directions. All the related resources of GraphRAG, including research papers, open-source data, and projects, are collected for the community in blue{https://github.com/DEEP-PolyU/Awesome-GraphRAG}.

We develop a novel policy synthesis algorithm, RMPflow, based on geometrically consistent transformations of Riemannian Motion Policies (RMPs). RMPs are a class of reactive motion policies designed to parameterize non-Euclidean behaviors as dynamical systems in intrinsically nonlinear task spaces. Given a set of RMPs designed for individual tasks, RMPflow can consistently combine these local policies to generate an expressive global policy, while simultaneously exploiting sparse structure for computational efficiency. We study the geometric properties of RMPflow and provide sufficient conditions for stability. Finally, we experimentally demonstrate that accounting for the geometry of task policies can simplify classically difficult problems, such as planning through clutter on high-DOF manipulation systems.

GraphRAG addresses significant challenges in Retrieval-Augmented Generation (RAG) by leveraging graphs with embedded knowledge to enhance the reasoning capabilities of Large Language Models (LLMs). Despite its promising potential, the GraphRAG community currently lacks a unified framework for fine-grained decomposition of the graph-based knowledge retrieval process. Furthermore, there is no systematic categorization or evaluation of existing solutions within the retrieval process. In this paper, we present LEGO-GraphRAG, a modular framework that decomposes the retrieval process of GraphRAG into three interconnected modules: subgraph-extraction, path-filtering, and path-refinement. We systematically summarize and classify the algorithms and neural network (NN) models relevant to each module, providing a clearer understanding of the design space for GraphRAG instances. Additionally, we identify key design factors, such as Graph Coupling and Computational Cost, that influence the effectiveness of GraphRAG implementations. Through extensive empirical studies, we construct high-quality GraphRAG instances using a representative selection of solutions and analyze their impact on retrieval and reasoning performance. Our findings offer critical insights into optimizing GraphRAG instance design, ultimately contributing to the advancement of more accurate and contextually relevant LLM applications.

Failure mode and effects analysis (FMEA) is a critical tool for mitigating potential failures, particular during ramp-up phases of new products. However, its effectiveness is often limited by the missing reasoning capabilities of the FMEA tools, which are usually tabular structured. Meanwhile, large language models (LLMs) offer novel prospects for fine-tuning on custom datasets for reasoning within FMEA contexts. However, LLMs face challenges in tasks that require factual knowledge, a gap that retrieval-augmented generation (RAG) approaches aim to fill. RAG retrieves information from a non-parametric data store and uses a language model to generate responses. Building on this idea, we propose to advance the non-parametric data store with a knowledge graph (KG). By enhancing the RAG framework with a KG, our objective is to leverage analytical and semantic question-answering capabilities on FMEA data. This paper contributes by presenting a new ontology for FMEA observations, an algorithm for creating vector embeddings from the FMEA KG, and a KG enhanced RAG framework. Our approach is validated through a human study and we measure the performance of the context retrieval recall and precision.

Graph-based retrieval-augmented generation (Graph-based RAG) has demonstrated significant potential in enhancing Large Language Models (LLMs) with structured knowledge. However, existing methods face three critical challenges: Inaccurate Graph Construction, caused by LLM hallucination; Poor Reasoning Ability, caused by failing to generate explicit reasons telling LLM why certain chunks were selected; and Inadequate Answering, which only partially answers the query due to the inadequate LLM reasoning, making their performance lag behind NaiveRAG on certain tasks. To address these issues, we propose AGRAG, an advanced graph-based retrieval-augmented generation framework. When constructing the graph, AGRAG substitutes the widely used LLM entity extraction method with a statistics-based method, avoiding hallucination and error propagation. When retrieval, AGRAG formulates the graph reasoning procedure as the Minimum Cost Maximum Influence (MCMI) subgraph generation problem, where we try to include more nodes with high influence score, but with less involving edge cost, to make the generated reasoning paths more comprehensive. We prove this problem to be NP-hard, and propose a greedy algorithm to solve it. The MCMI subgraph generated can serve as explicit reasoning paths to tell LLM why certain chunks were retrieved, thereby making the LLM better focus on the query-related part contents of the chunks, reducing the impact of noise, and improving AGRAG's reasoning ability. Furthermore, compared with the simple tree-structured reasoning paths, our MCMI subgraph can allow more complex graph structures, such as cycles, and improve the comprehensiveness of the generated reasoning paths.

Generating 3D scenes from natural language holds great promise for applications in gaming, film, and design. However, existing methods struggle with automation, 3D consistency, and fine-grained control. We present DreamScene, an end-to-end framework for high-quality and editable 3D scene generation from text or dialogue. DreamScene begins with a scene planning module, where a GPT-4 agent infers object semantics and spatial constraints to construct a hybrid graph. A graph-based placement algorithm then produces a structured, collision-free layout. Based on this layout, Formation Pattern Sampling (FPS) generates object geometry using multi-timestep sampling and reconstructive optimization, enabling fast and realistic synthesis. To ensure global consistent, DreamScene employs a progressive camera sampling strategy tailored to both indoor and outdoor settings. Finally, the system supports fine-grained scene editing, including object movement, appearance changes, and 4D dynamic motion. Experiments demonstrate that DreamScene surpasses prior methods in quality, consistency, and flexibility, offering a practical solution for open-domain 3D content creation. Code and demos are available at https://jahnsonblack.github.io/DreamScene-Full/.

Generating molecules that satisfy precise numeric constraints over multiple physicochemical properties is critical and challenging. Although large language models (LLMs) are expressive, they struggle with precise multi-objective control and numeric reasoning without external structure and feedback. We introduce M olGen, a fragment-level, retrieval-augmented, two-stage framework for molecule generation under multi-property constraints. Stage I : Prototype generation: a multi-agent reasoner performs retrieval-anchored, fragment-level edits to produce a candidate near the feasible region. Stage II : RL-based fine-grained optimization: a fragment-level optimizer trained with Group Relative Policy Optimization (GRPO) applies one- or multi-hop refinements to explicitly minimize the property errors toward our target while regulating edit complexity and deviation from the prototype. A large, automatically curated dataset with reasoning chains of fragment edits and measured property deltas underpins both stages, enabling deterministic, reproducible supervision and controllable multi-hop reasoning. Unlike prior work, our framework better reasons about molecules by leveraging fragments and supports controllable refinement toward numeric targets. Experiments on generation under two sets of property constraints (QED, LogP, Molecular Weight and HOMO, LUMO) show consistent gains in validity and precise satisfaction of multi-property targets, outperforming strong LLMs and graph-based algorithms.

A few-shot font generation (FFG) method has to satisfy two objectives: the generated images should preserve the underlying global structure of the target character and present the diverse local reference style. Existing FFG methods aim to disentangle content and style either by extracting a universal representation style or extracting multiple component-wise style representations. However, previous methods either fail to capture diverse local styles or cannot be generalized to a character with unseen components, e.g., unseen language systems. To mitigate the issues, we propose a novel FFG method, named Multiple Localized Experts Few-shot Font Generation Network (MX-Font). MX-Font extracts multiple style features not explicitly conditioned on component labels, but automatically by multiple experts to represent different local concepts, e.g., left-side sub-glyph. Owing to the multiple experts, MX-Font can capture diverse local concepts and show the generalizability to unseen languages. During training, we utilize component labels as weak supervision to guide each expert to be specialized for different local concepts. We formulate the component assign problem to each expert as the graph matching problem, and solve it by the Hungarian algorithm. We also employ the independence loss and the content-style adversarial loss to impose the content-style disentanglement. In our experiments, MX-Font outperforms previous state-of-the-art FFG methods in the Chinese generation and cross-lingual, e.g., Chinese to Korean, generation. Source code is available at https://github.com/clovaai/mxfont.

Graph generation with Machine Learning is an open problem with applications in various research fields. In this work, we propose to cast the generative process of a graph into a sequential one, relying on a node ordering procedure. We use this sequential process to design a novel generative model composed of two recurrent neural networks that learn to predict the edges of graphs: the first network generates one endpoint of each edge, while the second network generates the other endpoint conditioned on the state of the first. We test our approach extensively on five different datasets, comparing with two well-known baselines coming from graph literature, and two recurrent approaches, one of which holds state of the art performances. Evaluation is conducted considering quantitative and qualitative characteristics of the generated samples. Results show that our approach is able to yield novel, and unique graphs originating from very different distributions, while retaining structural properties very similar to those in the training sample. Under the proposed evaluation framework, our approach is able to reach performances comparable to the current state of the art on the graph generation task.

In the realm of generative models for graphs, extensive research has been conducted. However, most existing methods struggle with large graphs due to the complexity of representing the entire joint distribution across all node pairs and capturing both global and local graph structures simultaneously. To overcome these issues, we introduce a method that generates a graph by progressively expanding a single node to a target graph. In each step, nodes and edges are added in a localized manner through denoising diffusion, building first the global structure, and then refining the local details. The local generation avoids modeling the entire joint distribution over all node pairs, achieving substantial computational savings with subquadratic runtime relative to node count while maintaining high expressivity through multiscale generation. Our experiments show that our model achieves state-of-the-art performance on well-established benchmark datasets while successfully scaling to graphs with at least 5000 nodes. Our method is also the first to successfully extrapolate to graphs outside of the training distribution, showcasing a much better generalization capability over existing methods.

Graph generation is a critical task in numerous domains, including molecular design and social network analysis, due to its ability to model complex relationships and structured data. While most modern graph generative models utilize adjacency matrix representations, this work revisits an alternative approach that represents graphs as sequences of node set and edge set. We advocate for this approach due to its efficient encoding of graphs and propose a novel representation. Based on this representation, we introduce the Graph Generative Pre-trained Transformer (G2PT), an auto-regressive model that learns graph structures via next-token prediction. To further exploit G2PT's capabilities as a general-purpose foundation model, we explore fine-tuning strategies for two downstream applications: goal-oriented generation and graph property prediction. We conduct extensive experiments across multiple datasets. Results indicate that G2PT achieves superior generative performance on both generic graph and molecule datasets. Furthermore, G2PT exhibits strong adaptability and versatility in downstream tasks from molecular design to property prediction.

Recently, there has been a surge of interest in employing neural networks for graph generation, a fundamental statistical learning problem with critical applications like molecule design and community analysis. However, most approaches encounter significant limitations when generating large-scale graphs. This is due to their requirement to output the full adjacency matrices whose size grows quadratically with the number of nodes. In response to this challenge, we introduce a new, simple, and scalable graph representation named gap encoded edge list (GEEL) that has a small representation size that aligns with the number of edges. In addition, GEEL significantly reduces the vocabulary size by incorporating the gap encoding and bandwidth restriction schemes. GEEL can be autoregressively generated with the incorporation of node positional encoding, and we further extend GEEL to deal with attributed graphs by designing a new grammar. Our findings reveal that the adoption of this compact representation not only enhances scalability but also bolsters performance by simplifying the graph generation process. We conduct a comprehensive evaluation across ten non-attributed and two molecular graph generation tasks, demonstrating the effectiveness of GEEL.

Most real-world graphs exhibit a hierarchical structure, which is often overlooked by existing graph generation methods. To address this limitation, we propose a novel graph generative network that captures the hierarchical nature of graphs and successively generates the graph sub-structures in a coarse-to-fine fashion. At each level of hierarchy, this model generates communities in parallel, followed by the prediction of cross-edges between communities using separate neural networks. This modular approach enables scalable graph generation for large and complex graphs. Moreover, we model the output distribution of edges in the hierarchical graph with a multinomial distribution and derive a recursive factorization for this distribution. This enables us to generate community graphs with integer-valued edge weights in an autoregressive manner. Empirical studies demonstrate the effectiveness and scalability of our proposed generative model, achieving state-of-the-art performance in terms of graph quality across various benchmark datasets. The code is available at https://github.com/Karami-m/HiGen_main.

Recent advancements in large language models (LLMs) have shown impressive versatility across various tasks. To eliminate its hallucinations, retrieval-augmented generation (RAG) has emerged as a powerful approach, leveraging external knowledge sources like knowledge graphs (KGs). In this paper, we study the task of KG-driven RAG and propose a novel Similar Graph Enhanced Retrieval-Augmented Generation (SimGRAG) method. It effectively addresses the challenge of aligning query texts and KG structures through a two-stage process: (1) query-to-pattern, which uses an LLM to transform queries into a desired graph pattern, and (2) pattern-to-subgraph, which quantifies the alignment between the pattern and candidate subgraphs using a graph semantic distance (GSD) metric. We also develop an optimized retrieval algorithm that efficiently identifies the top-k subgraphs within 1-second latency on a 10-million-scale KG. Extensive experiments show that SimGRAG outperforms state-of-the-art KG-driven RAG methods in both question answering and fact verification, offering superior plug-and-play usability and scalability.

This tutorial serves as a comprehensive guide for understanding graph databases, focusing on the fundamentals of graph theory while showcasing practical applications across various fields. It starts by introducing foundational concepts and delves into the structure of graphs through nodes and edges, covering different types such as undirected, directed, weighted, and unweighted graphs. Key graph properties, terminologies, and essential algorithms for network analysis are outlined, including Dijkstras shortest path algorithm and methods for calculating node centrality and graph connectivity. The tutorial highlights the advantages of graph databases over traditional relational databases, particularly in efficiently managing complex, interconnected data. It examines leading graph database systems such as Neo4j, Amazon Neptune, and ArangoDB, emphasizing their unique features for handling large datasets. Practical instructions on graph operations using NetworkX and Neo4j are provided, covering node and edge creation, attribute assignment, and advanced queries with Cypher. Additionally, the tutorial explores common graph visualization techniques using tools like Plotly and Neo4j Bloom, which enhance the interpretation and usability of graph data. It also delves into community detection algorithms, including the Louvain method, which facilitates clustering in large networks. Finally, the paper concludes with recommendations for researchers interested in exploring the vast potential of graph technologies.

Understanding and navigating large-scale codebases remains a significant challenge in software engineering. Existing methods often treat code as flat text or focus primarily on local structural relationships, limiting their ability to provide holistic, context-aware information retrieval. We present Hierarchical Code Graph Summarization (HCGS), a novel approach that constructs a multi-layered representation of a codebase by generating structured summaries in a bottom-up fashion from a code graph. HCGS leverages the Language Server Protocol for language-agnostic code analysis and employs a parallel level-based algorithm for efficient summary generation. Through extensive evaluation on five diverse codebases totaling 7,531 functions, HCGS demonstrates significant improvements in code retrieval accuracy, achieving up to 82 percentage relative improvement in top-1 retrieval precision for large codebases like libsignal (27.15 percentage points), and perfect Pass@3 scores for smaller repositories. The system's hierarchical approach consistently outperforms traditional code-only retrieval across all metrics, with particularly substantial gains in larger, more complex codebases where understanding function relationships is crucial.

Graph generation is integral to various engineering and scientific disciplines. Nevertheless, existing methodologies tend to overlook the generation of edge attributes. However, we identify critical applications where edge attributes are essential, making prior methods potentially unsuitable in such contexts. Moreover, while trivial adaptations are available, empirical investigations reveal their limited efficacy as they do not properly model the interplay among graph components. To address this, we propose a joint score-based model of nodes and edges for graph generation that considers all graph components. Our approach offers two key novelties: (i) node and edge attributes are combined in an attention module that generates samples based on the two ingredients; and (ii) node, edge and adjacency information are mutually dependent during the graph diffusion process. We evaluate our method on challenging benchmarks involving real-world and synthetic datasets in which edge features are crucial. Additionally, we introduce a new synthetic dataset that incorporates edge values. Furthermore, we propose a novel application that greatly benefits from the method due to its nature: the generation of traffic scenes represented as graphs. Our method outperforms other graph generation methods, demonstrating a significant advantage in edge-related measures.

Automatic Speaker Verification (ASV) systems, which identify speakers based on their voice characteristics, have numerous applications, such as user authentication in financial transactions, exclusive access control in smart devices, and forensic fraud detection. However, the advancement of deep learning algorithms has enabled the generation of synthetic audio through Text-to-Speech (TTS) and Voice Conversion (VC) systems, exposing ASV systems to potential vulnerabilities. To counteract this, we propose a novel architecture named AASIST3. By enhancing the existing AASIST framework with Kolmogorov-Arnold networks, additional layers, encoders, and pre-emphasis techniques, AASIST3 achieves a more than twofold improvement in performance. It demonstrates minDCF results of 0.5357 in the closed condition and 0.1414 in the open condition, significantly enhancing the detection of synthetic voices and improving ASV security.

Generating graph-structured data requires learning the underlying distribution of graphs. Yet, this is a challenging problem, and the previous graph generative methods either fail to capture the permutation-invariance property of graphs or cannot sufficiently model the complex dependency between nodes and edges, which is crucial for generating real-world graphs such as molecules. To overcome such limitations, we propose a novel score-based generative model for graphs with a continuous-time framework. Specifically, we propose a new graph diffusion process that models the joint distribution of the nodes and edges through a system of stochastic differential equations (SDEs). Then, we derive novel score matching objectives tailored for the proposed diffusion process to estimate the gradient of the joint log-density with respect to each component, and introduce a new solver for the system of SDEs to efficiently sample from the reverse diffusion process. We validate our graph generation method on diverse datasets, on which it either achieves significantly superior or competitive performance to the baselines. Further analysis shows that our method is able to generate molecules that lie close to the training distribution yet do not violate the chemical valency rule, demonstrating the effectiveness of the system of SDEs in modeling the node-edge relationships. Our code is available at https://github.com/harryjo97/GDSS.

Recently, Vision Language Models (VLMs) have experienced significant advancements, yet these models still face challenges in spatial hierarchical reasoning within indoor scenes. In this study, we introduce ROOT, a VLM-based system designed to enhance the analysis of indoor scenes. Specifically, we first develop an iterative object perception algorithm using GPT-4V to detect object entities within indoor scenes. This is followed by employing vision foundation models to acquire additional meta-information about the scene, such as bounding boxes. Building on this foundational data, we propose a specialized VLM, SceneVLM, which is capable of generating spatial hierarchical scene graphs and providing distance information for objects within indoor environments. This information enhances our understanding of the spatial arrangement of indoor scenes. To train our SceneVLM, we collect over 610,000 images from various public indoor datasets and implement a scene data generation pipeline with a semi-automated technique to establish relationships and estimate distances among indoor objects. By utilizing this enriched data, we conduct various training recipes and finish SceneVLM. Our experiments demonstrate that \rootname facilitates indoor scene understanding and proves effective in diverse downstream applications, such as 3D scene generation and embodied AI. The code will be released at https://github.com/harrytea/ROOT.

Generation of graphs is a major challenge for real-world tasks that require understanding the complex nature of their non-Euclidean structures. Although diffusion models have achieved notable success in graph generation recently, they are ill-suited for modeling the topological properties of graphs since learning to denoise the noisy samples does not explicitly learn the graph structures to be generated. To tackle this limitation, we propose a generative framework that models the topology of graphs by explicitly learning the final graph structures of the diffusion process. Specifically, we design the generative process as a mixture of endpoint-conditioned diffusion processes which is driven toward the predicted graph that results in rapid convergence. We further introduce a simple parameterization of the mixture process and develop an objective for learning the final graph structure, which enables maximum likelihood training. Through extensive experimental validation on general graph and 2D/3D molecule generation tasks, we show that our method outperforms previous generative models, generating graphs with correct topology with both continuous (e.g. 3D coordinates) and discrete (e.g. atom types) features. Our code is available at https://github.com/harryjo97/GruM.

This work studies a central extremal graph theory problem inspired by a 1975 conjecture of Erdos, which aims to find graphs with a given size (number of nodes) that maximize the number of edges without having 3- or 4-cycles. We formulate this problem as a sequential decision-making problem and compare AlphaZero, a neural network-guided tree search, with tabu search, a heuristic local search method. Using either method, by introducing a curriculum -- jump-starting the search for larger graphs using good graphs found at smaller sizes -- we improve the state-of-the-art lower bounds for several sizes. We also propose a flexible graph-generation environment and a permutation-invariant network architecture for learning to search in the space of graphs.

Being the most cutting-edge generative methods, diffusion methods have shown great advances in wide generation tasks. Among them, graph generation attracts significant research attention for its broad application in real life. In our survey, we systematically and comprehensively review on diffusion-based graph generative methods. We first make a review on three mainstream paradigms of diffusion methods, which are denoising diffusion probabilistic models, score-based genrative models, and stochastic differential equations. Then we further categorize and introduce the latest applications of diffusion models on graphs. In the end, we point out some limitations of current studies and future directions of future explorations. The summary of existing methods metioned in this survey is in https://github.com/zhejiangzhuque/Diffusion-based-Graph-Generative-Methods.

Diffusion models, as a novel generative paradigm, have achieved remarkable success in various image generation tasks such as image inpainting, image-to-text translation, and video generation. Graph generation is a crucial computational task on graphs with numerous real-world applications. It aims to learn the distribution of given graphs and then generate new graphs. Given the great success of diffusion models in image generation, increasing efforts have been made to leverage these techniques to advance graph generation in recent years. In this paper, we first provide a comprehensive overview of generative diffusion models on graphs, In particular, we review representative algorithms for three variants of graph diffusion models, i.e., Score Matching with Langevin Dynamics (SMLD), Denoising Diffusion Probabilistic Model (DDPM), and Score-based Generative Model (SGM). Then, we summarize the major applications of generative diffusion models on graphs with a specific focus on molecule and protein modeling. Finally, we discuss promising directions in generative diffusion models on graph-structured data. For this survey, we also created a GitHub project website by collecting the supporting resources for generative diffusion models on graphs, at the link: https://github.com/ChengyiLIU-cs/Generative-Diffusion-Models-on-Graphs

Deep graph generative modeling has proven capable of learning the distribution of complex, multi-scale structures characterizing real-world graphs. However, one of the main limitations of existing methods is their large output space, which limits generation scalability and hinders accurate modeling of the underlying distribution. To overcome these limitations, we propose a novel approach that significantly reduces the output space of existing graph generative models. Specifically, starting from the observation that many real-world graphs have low graph bandwidth, we restrict graph bandwidth during training and generation. Our strategy improves both generation scalability and quality without increasing architectural complexity or reducing expressiveness. Our approach is compatible with existing graph generative methods, and we describe its application to both autoregressive and one-shot models. We extensively validate our strategy on synthetic and real datasets, including molecular graphs. Our experiments show that, in addition to improving generation efficiency, our approach consistently improves generation quality and reconstruction accuracy. The implementation is made available.

Diffusion-based generative graph models have been proven effective in generating high-quality small graphs. However, they need to be more scalable for generating large graphs containing thousands of nodes desiring graph statistics. In this work, we propose EDGE, a new diffusion-based generative graph model that addresses generative tasks with large graphs. To improve computation efficiency, we encourage graph sparsity by using a discrete diffusion process that randomly removes edges at each time step and finally obtains an empty graph. EDGE only focuses on a portion of nodes in the graph at each denoising step. It makes much fewer edge predictions than previous diffusion-based models. Moreover, EDGE admits explicitly modeling the node degrees of the graphs, further improving the model performance. The empirical study shows that EDGE is much more efficient than competing methods and can generate large graphs with thousands of nodes. It also outperforms baseline models in generation quality: graphs generated by our approach have more similar graph statistics to those of the training graphs.

A subgraph is constructed by using a subset of vertices and edges of a given graph. There exist many graph properties that are hereditary for subgraphs. Hence, researchers from different communities have paid a great deal of attention in studying numerous subgraph problems, on top of the ordinary graph problems. Many algorithms are proposed in studying subgraph problems, where one common approach is by extracting the patterns and structures of a given graph. Due to the complex structures of certain types of graphs and to improve overall performances of the existing frameworks, machine learning techniques have recently been employed in dealing with various subgraph problems. In this article, we present a comprehensive review on five well known subgraph problems that have been tackled by using machine learning methods. They are subgraph isomorphism (both counting and matching), maximum common subgraph, community detection and community search problems. We provide an outline of each proposed method, and examine its designs and performances. We also explore non-learning-based algorithms for each problem and a brief discussion is given. We then suggest some promising research directions in this area, hoping that relevant subgraph problems can be tackled by using a similar strategy. Since there is a huge growth in employing machine learning techniques in recent years, we believe that this survey will serve as a good reference point to relevant research communities.

Graphs or networks are a very convenient way to represent data with lots of interaction. Recently, Machine Learning on Graph data has gained a lot of traction. In particular, vertex classification and missing edge detection have very interesting applications, ranging from drug discovery to recommender systems. To achieve such tasks, tremendous work has been accomplished to learn embedding of nodes and edges into finite-dimension vector spaces. This task is called Graph Representation Learning. However, Graph Representation Learning techniques often display prohibitive time and memory complexities, preventing their use in real-time with business size graphs. In this paper, we address this issue by leveraging a degeneracy property of Graphs - the K-Core Decomposition. We present two techniques taking advantage of this decomposition to reduce the time and memory consumption of walk-based Graph Representation Learning algorithms. We evaluate the performances, expressed in terms of quality of embedding and computational resources, of the proposed techniques on several academic datasets. Our code is available at https://github.com/SBrandeis/kcore-embedding

Graphs can be used to represent and reason about systems and a variety of metrics have been devised to quantify their global characteristics. However, little is currently known about how to construct a graph or improve an existing one given a target objective. In this work, we formulate the construction of a graph as a decision-making process in which a central agent creates topologies by trial and error and receives rewards proportional to the value of the target objective. By means of this conceptual framework, we propose an algorithm based on reinforcement learning and graph neural networks to learn graph construction and improvement strategies. Our core case study focuses on robustness to failures and attacks, a property relevant for the infrastructure and communication networks that power modern society. Experiments on synthetic and real-world graphs show that this approach can outperform existing methods while being cheaper to evaluate. It also allows generalization to out-of-sample graphs, as well as to larger out-of-distribution graphs in some cases. The approach is applicable to the optimization of other global structural properties of graphs.

Graph neural networks (GNNs) have been demonstrated to be powerful in modeling graph-structured data. However, training GNNs usually requires abundant task-specific labeled data, which is often arduously expensive to obtain. One effective way to reduce the labeling effort is to pre-train an expressive GNN model on unlabeled data with self-supervision and then transfer the learned model to downstream tasks with only a few labels. In this paper, we present the GPT-GNN framework to initialize GNNs by generative pre-training. GPT-GNN introduces a self-supervised attributed graph generation task to pre-train a GNN so that it can capture the structural and semantic properties of the graph. We factorize the likelihood of the graph generation into two components: 1) Attribute Generation and 2) Edge Generation. By modeling both components, GPT-GNN captures the inherent dependency between node attributes and graph structure during the generative process. Comprehensive experiments on the billion-scale Open Academic Graph and Amazon recommendation data demonstrate that GPT-GNN significantly outperforms state-of-the-art GNN models without pre-training by up to 9.1% across various downstream tasks.

The automated extraction of complete and precise road network graphs from remote sensing imagery remains a critical challenge in geospatial computer vision. Segmentation-based approaches, while effective in pixel-level recognition, struggle to maintain topology fidelity after vectorization postprocessing. Graph-growing methods build more topologically faithful graphs but suffer from computationally prohibitive iterative ROI cropping. Graph-generating methods first predict global static candidate road network vertices, and then infer possible edges between vertices. They achieve fast topology-aware inference, but limits the dynamic insertion of vertices. To address these challenges, we propose DeH4R, a novel hybrid model that combines graph-generating efficiency and graph-growing dynamics. This is achieved by decoupling the task into candidate vertex detection, adjacent vertex prediction, initial graph contruction, and graph expansion. This architectural innovation enables dynamic vertex (edge) insertions while retaining fast inference speed and enhancing both topology fidelity and spatial consistency. Comprehensive evaluations on CityScale and SpaceNet benchmarks demonstrate state-of-the-art (SOTA) performance. DeH4R outperforms the prior SOTA graph-growing method RNGDet++ by 4.62 APLS and 10.18 IoU on CityScale, while being approximately 10 times faster. The code will be made publicly available at https://github.com/7777777FAN/DeH4R.

In recent years, many large directed networks such as online social networks are collected with the help of powerful data engineering and data storage techniques. Analyses of such networks attract significant attention from both the academics and industries. However, analyses of large directed networks are often time-consuming and expensive because the complexities of a lot of graph algorithms are often polynomial with the size of the graph. Hence, sampling algorithms that can generate graphs preserving properties of original graph are of great importance because they can speed up the analysis process. We propose a promising framework to sample directed graphs: Construct a sample graph with linearly rescaled Joint Degree Matrix (JDM) and Degree Correlation Matrix (DCM). Previous work shows that graphs with the same JDM and DCM will have a range of very similar graph properties. We also conduct experiments on real-world datasets to show that the numbers of non-zero entries in JDM and DCM are quite small compared to the number of edges and nodes. Adopting this framework, we propose a novel graph sampling algorithm that can provably preserves in-degree and out-degree distributions, which are two most fundamental properties of a graph. We also prove the upper bound for deviations in the joint degree distribution and degree correlation distribution, which correspond to JDM and DCM. Besides, we prove that the deviations in these distributions are negatively correlated with the sparsity of the JDM and DCM. Considering that these two matrices are always quite sparse, we believe that proposed algorithm will have a better-than-theory performance on real-world large directed networks.

Network embedding has been intensively studied in the literature and widely used in various applications, such as link prediction and node classification. While previous work focus on the design of new algorithms or are tailored for various problem settings, the discussion of initialization strategies in the learning process is often missed. In this work, we address this important issue of initialization for network embedding that could dramatically improve the performance of the algorithms on both effectiveness and efficiency. Specifically, we first exploit the graph partition technique that divides the graph into several disjoint subsets, and then construct an abstract graph based on the partitions. We obtain the initialization of the embedding for each node in the graph by computing the network embedding on the abstract graph, which is much smaller than the input graph, and then propagating the embedding among the nodes in the input graph. With extensive experiments on various datasets, we demonstrate that our initialization technique significantly improves the performance of the state-of-the-art algorithms on the evaluations of link prediction and node classification by up to 7.76% and 8.74% respectively. Besides, we show that the technique of initialization reduces the running time of the state-of-the-arts by at least 20%.

The execution of graph algorithms using neural networks has recently attracted significant interest due to promising empirical progress. This motivates further understanding of how neural networks can replicate reasoning steps with relational data. In this work, we study the ability of transformer networks to simulate algorithms on graphs from a theoretical perspective. The architecture that we utilize is a looped transformer with extra attention heads that interact with the graph. We prove by construction that this architecture can simulate algorithms such as Dijkstra's shortest path algorithm, Breadth- and Depth-First Search, and Kosaraju's strongly connected components algorithm. The width of the network does not increase with the size of the input graph, which implies that the network can simulate the above algorithms for any graph. Despite this property, we show that there is a limit to simulation in our solution due to finite precision. Finally, we show a Turing Completeness result with constant width when the extra attention heads are utilized.

Large language models (LLMs) are increasingly adopted for a variety of tasks with implicit graphical structures, such as planning in robotics, multi-hop question answering or knowledge probing, structured commonsense reasoning, and more. While LLMs have advanced the state-of-the-art on these tasks with structure implications, whether LLMs could explicitly process textual descriptions of graphs and structures, map them to grounded conceptual spaces, and perform structured operations remains underexplored. To this end, we propose NLGraph (Natural Language Graph), a comprehensive benchmark of graph-based problem solving designed in natural language. NLGraph contains 29,370 problems, covering eight graph reasoning tasks with varying complexity from simple tasks such as connectivity and shortest path up to complex problems such as maximum flow and simulating graph neural networks. We evaluate LLMs (GPT-3/4) with various prompting approaches on the NLGraph benchmark and find that 1) language models do demonstrate preliminary graph reasoning abilities, 2) the benefit of advanced prompting and in-context learning diminishes on more complex graph problems, while 3) LLMs are also (un)surprisingly brittle in the face of spurious correlations in graph and problem settings. We then propose Build-a-Graph Prompting and Algorithmic Prompting, two instruction-based approaches to enhance LLMs in solving natural language graph problems. Build-a-Graph and Algorithmic prompting improve the performance of LLMs on NLGraph by 3.07% to 16.85% across multiple tasks and settings, while how to solve the most complicated graph reasoning tasks in our setup with language models remains an open research question. The NLGraph benchmark and evaluation code are available at https://github.com/Arthur-Heng/NLGraph.

Graph generative models become increasingly effective for data distribution approximation and data augmentation. While they have aroused public concerns about their malicious misuses or misinformation broadcasts, just as what Deepfake visual and auditory media has been delivering to society. Hence it is essential to regulate the prevalence of generated graphs. To tackle this problem, we pioneer the formulation of the generated graph detection problem to distinguish generated graphs from real ones. We propose the first framework to systematically investigate a set of sophisticated models and their performance in four classification scenarios. Each scenario switches between seen and unseen datasets/generators during testing to get closer to real-world settings and progressively challenge the classifiers. Extensive experiments evidence that all the models are qualified for generated graph detection, with specific models having advantages in specific scenarios. Resulting from the validated generality and oblivion of the classifiers to unseen datasets/generators, we draw a safe conclusion that our solution can sustain for a decent while to curb generated graph misuses.

Evaluating and enhancing the general capabilities of large language models (LLMs) has been an important research topic. Graph is a common data structure in the real world, and understanding graph data is a crucial part for advancing general intelligence. To evaluate and enhance the graph understanding abilities of LLMs, in this paper, we propose a benchmark named GraphInstruct, which comprehensively includes 21 classical graph reasoning tasks, providing diverse graph generation pipelines and detailed reasoning steps. Based on GraphInstruct, we further construct GraphLM through efficient instruction-tuning, which shows prominent graph understanding capability. In order to enhance the LLM with graph reasoning capability as well, we propose a step mask training strategy, and construct a model named GraphLM+. As one of the pioneering efforts to enhance the graph understanding and reasoning abilities of LLMs, extensive experiments have demonstrated the superiority of GraphLM and GraphLM+ over other LLMs. We look forward to more researchers exploring the potential of LLMs in the graph data mining domain through GraphInstruct. Our code for generating GraphInstruct is released publicly at: https://github.com/CGCL-codes/GraphInstruct.

Graph Neural Networks (GNNs) are popular models for graph learning problems. GNNs show strong empirical performance in many practical tasks. However, the theoretical properties have not been completely elucidated. In this paper, we investigate whether GNNs can exploit the graph structure from the perspective of the expressive power of GNNs. In our analysis, we consider graph generation processes that are controlled by hidden (or latent) node features, which contain all information about the graph structure. A typical example of this framework is kNN graphs constructed from the hidden features. In our main results, we show that GNNs can recover the hidden node features from the input graph alone, even when all node features, including the hidden features themselves and any indirect hints, are unavailable. GNNs can further use the recovered node features for downstream tasks. These results show that GNNs can fully exploit the graph structure by themselves, and in effect, GNNs can use both the hidden and explicit node features for downstream tasks. In the experiments, we confirm the validity of our results by showing that GNNs can accurately recover the hidden features using a GNN architecture built based on our theoretical analysis.

Pre-trained sequence-to-sequence language models have led to widespread success in many natural language generation tasks. However, there has been relatively less work on analyzing their ability to generate structured outputs such as graphs. Unlike natural language, graphs have distinct structural and semantic properties in the context of a downstream NLP task, e.g., generating a graph that is connected and acyclic can be attributed to its structural constraints, while the semantics of a graph can refer to how meaningfully an edge represents the relation between two node concepts. In this work, we study pre-trained language models that generate explanation graphs in an end-to-end manner and analyze their ability to learn the structural constraints and semantics of such graphs. We first show that with limited supervision, pre-trained language models often generate graphs that either violate these constraints or are semantically incoherent. Since curating large amount of human-annotated graphs is expensive and tedious, we propose simple yet effective ways of graph perturbations via node and edge edit operations that lead to structurally and semantically positive and negative graphs. Next, we leverage these graphs in different contrastive learning models with Max-Margin and InfoNCE losses. Our methods lead to significant improvements in both structural and semantic accuracy of explanation graphs and also generalize to other similar graph generation tasks. Lastly, we show that human errors are the best negatives for contrastive learning and also that automatically generating more such human-like negative graphs can lead to further improvements. Our code and models are publicly available at https://github.com/swarnaHub/ExplagraphGen

Advancements in generative models have sparked significant interest in generating images while adhering to specific structural guidelines. Scene graph to image generation is one such task of generating images which are consistent with the given scene graph. However, the complexity of visual scenes poses a challenge in accurately aligning objects based on specified relations within the scene graph. Existing methods approach this task by first predicting a scene layout and generating images from these layouts using adversarial training. In this work, we introduce a novel approach to generate images from scene graphs which eliminates the need of predicting intermediate layouts. We leverage pre-trained text-to-image diffusion models and CLIP guidance to translate graph knowledge into images. Towards this, we first pre-train our graph encoder to align graph features with CLIP features of corresponding images using a GAN based training. Further, we fuse the graph features with CLIP embedding of object labels present in the given scene graph to create a graph consistent CLIP guided conditioning signal. In the conditioning input, object embeddings provide coarse structure of the image and graph features provide structural alignment based on relationships among objects. Finally, we fine tune a pre-trained diffusion model with the graph consistent conditioning signal with reconstruction and CLIP alignment loss. Elaborate experiments reveal that our method outperforms existing methods on standard benchmarks of COCO-stuff and Visual Genome dataset.

Large Generative Models (LGMs) such as GPT, Stable Diffusion, Sora, and Suno are trained on a huge amount of language corpus, images, videos, and audio that are extremely diverse from numerous domains. This training paradigm over diverse well-curated data lies at the heart of generating creative and sensible content. However, all previous graph generative models (e.g., GraphRNN, MDVAE, MoFlow, GDSS, and DiGress) have been trained only on one dataset each time, which cannot replicate the revolutionary success achieved by LGMs in other fields. To remedy this crucial gap, we propose a new class of graph generative model called Large Graph Generative Model (LGGM) that is trained on a large corpus of graphs (over 5000 graphs) from 13 different domains. We empirically demonstrate that the pre-trained LGGM has superior zero-shot generative capability to existing graph generative models. Furthermore, our pre-trained LGGM can be easily fine-tuned with graphs from target domains and demonstrate even better performance than those directly trained from scratch, behaving as a solid starting point for real-world customization. Inspired by Stable Diffusion, we further equip LGGM with the capability to generate graphs given text prompts (Text-to-Graph), such as the description of the network name and domain (i.e., "The power-1138-bus graph represents a network of buses in a power distribution system."), and network statistics (i.e., "The graph has a low average degree, suitable for modeling social media interactions."). This Text-to-Graph capability integrates the extensive world knowledge in the underlying language model, offering users fine-grained control of the generated graphs. We release the code, the model checkpoint, and the datasets at https://lggm-lg.github.io/.

Generating 3D models lies at the core of computer graphics and has been the focus of decades of research. With the emergence of advanced neural representations and generative models, the field of 3D content generation is developing rapidly, enabling the creation of increasingly high-quality and diverse 3D models. The rapid growth of this field makes it difficult to stay abreast of all recent developments. In this survey, we aim to introduce the fundamental methodologies of 3D generation methods and establish a structured roadmap, encompassing 3D representation, generation methods, datasets, and corresponding applications. Specifically, we introduce the 3D representations that serve as the backbone for 3D generation. Furthermore, we provide a comprehensive overview of the rapidly growing literature on generation methods, categorized by the type of algorithmic paradigms, including feedforward generation, optimization-based generation, procedural generation, and generative novel view synthesis. Lastly, we discuss available datasets, applications, and open challenges. We hope this survey will help readers explore this exciting topic and foster further advancements in the field of 3D content generation.

In this paper, we present a novel generative task: joint scene graph - image generation. While previous works have explored image generation conditioned on scene graphs or layouts, our task is distinctive and important as it involves generating scene graphs themselves unconditionally from noise, enabling efficient and interpretable control for image generation. Our task is challenging, requiring the generation of plausible scene graphs with heterogeneous attributes for nodes (objects) and edges (relations among objects), including continuous object bounding boxes and discrete object and relation categories. We introduce a novel diffusion model, DiffuseSG, that jointly models the adjacency matrix along with heterogeneous node and edge attributes. We explore various types of encodings for the categorical data, relaxing it into a continuous space. With a graph transformer being the denoiser, DiffuseSG successively denoises the scene graph representation in a continuous space and discretizes the final representation to generate the clean scene graph. Additionally, we introduce an IoU regularization to enhance the empirical performance. Our model significantly outperforms existing methods in scene graph generation on the Visual Genome and COCO-Stuff datasets, both on standard and newly introduced metrics that better capture the problem complexity. Moreover, we demonstrate the additional benefits of our model in two downstream applications: 1) excelling in a series of scene graph completion tasks, and 2) improving scene graph detection models by using extra training samples generated from DiffuseSG.

Learning graph generative models over latent spaces has received less attention compared to models that operate on the original data space and has so far demonstrated lacklustre performance. We present GLAD a latent space graph generative model. Unlike most previous latent space graph generative models, GLAD operates on a discrete latent space that preserves to a significant extent the discrete nature of the graph structures making no unnatural assumptions such as latent space continuity. We learn the prior of our discrete latent space by adapting diffusion bridges to its structure. By operating over an appropriately constructed latent space we avoid relying on decompositions that are often used in models that operate in the original data space. We present experiments on a series of graph benchmark datasets which clearly show the superiority of the discrete latent space and obtain state of the art graph generative performance, making GLAD the first latent space graph generative model with competitive performance. Our source code is published at: https://github.com/v18nguye/GLAD.

Graph In-Context Learning, with the ability to adapt pre-trained graph models to novel and diverse downstream graphs without updating any parameters, has gained much attention in the community. The key to graph in-context learning is to perform downstream graphs conditioned on chosen prompt examples. Existing methods randomly select subgraphs or edges as prompts, leading to noisy graph prompts and inferior model performance. Additionally, due to the gap between pre-training and testing graphs, when the number of classes in the testing graphs is much greater than that in the training, the in-context learning ability will also significantly deteriorate. To tackle the aforementioned challenges, we develop a multi-stage adaptive prompt optimization method GraphPrompter, which optimizes the entire process of generating, selecting, and using graph prompts for better in-context learning capabilities. Firstly, Prompt Generator introduces a reconstruction layer to highlight the most informative edges and reduce irrelevant noise for graph prompt construction. Furthermore, in the selection stage, Prompt Selector employs the k-nearest neighbors algorithm and pre-trained selection layers to dynamically choose appropriate samples and minimize the influence of irrelevant prompts. Finally, we leverage a Prompt Augmenter with a cache replacement strategy to enhance the generalization capability of the pre-trained model on new datasets. Extensive experiments show that GraphPrompter effectively enhances the in-context learning ability of graph models. On average across all the settings, our approach surpasses the state-of-the-art baselines by over 8%. Our code is released at https://github.com/karin0018/GraphPrompter.

Artificial general intelligence on graphs has shown significant advancements across various applications, yet the traditional 'Pre-train & Fine-tune' paradigm faces inefficiencies and negative transfer issues, particularly in complex and few-shot settings. Graph prompt learning emerges as a promising alternative, leveraging lightweight prompts to manipulate data and fill the task gap by reformulating downstream tasks to the pretext. However, several critical challenges still remain: how to unify diverse graph prompt models, how to evaluate the quality of graph prompts, and to improve their usability for practical comparisons and selection. In response to these challenges, we introduce the first comprehensive benchmark for graph prompt learning. Our benchmark integrates SIX pre-training methods and FIVE state-of-the-art graph prompt techniques, evaluated across FIFTEEN diverse datasets to assess performance, flexibility, and efficiency. We also present 'ProG', an easy-to-use open-source library that streamlines the execution of various graph prompt models, facilitating objective evaluations. Additionally, we propose a unified framework that categorizes existing graph prompt methods into two main approaches: prompts as graphs and prompts as tokens. This framework enhances the applicability and comparison of graph prompt techniques. The code is available at: https://github.com/sheldonresearch/ProG.

This paper studies the problem of embedding very large information networks into low-dimensional vector spaces, which is useful in many tasks such as visualization, node classification, and link prediction. Most existing graph embedding methods do not scale for real world information networks which usually contain millions of nodes. In this paper, we propose a novel network embedding method called the "LINE," which is suitable for arbitrary types of information networks: undirected, directed, and/or weighted. The method optimizes a carefully designed objective function that preserves both the local and global network structures. An edge-sampling algorithm is proposed that addresses the limitation of the classical stochastic gradient descent and improves both the effectiveness and the efficiency of the inference. Empirical experiments prove the effectiveness of the LINE on a variety of real-world information networks, including language networks, social networks, and citation networks. The algorithm is very efficient, which is able to learn the embedding of a network with millions of vertices and billions of edges in a few hours on a typical single machine. The source code of the LINE is available online.

In this paper, we propose the first framework that enables solving graph learning tasks of all levels (node, edge and graph) and all types (generation, regression and classification) with one model. We first propose Latent Graph Diffusion (LGD), a generative model that can generate node, edge, and graph-level features of all categories simultaneously. We achieve this goal by embedding the graph structures and features into a latent space leveraging a powerful encoder which can also be decoded, then training a diffusion model in the latent space. LGD is also capable of conditional generation through a specifically designed cross-attention mechanism. Then we formulate prediction tasks including regression and classification as (conditional) generation, which enables our LGD to solve tasks of all levels and all types with provable guarantees. We verify the effectiveness of our framework with extensive experiments, where our models achieve state-of-the-art or highly competitive results across generation and regression tasks.

In recent years, Graph Neural Networks (GNNs) have made significant advances in processing structured data. However, most of them primarily adopted a model-centric approach, which simplifies graphs by converting them into undirected formats and emphasizes model designs. This approach is inherently limited in real-world applications due to the unavoidable information loss in simple undirected graphs and the model optimization challenges that arise when exceeding the upper bounds of this sub-optimal data representational capacity. As a result, there has been a shift toward data-centric methods that prioritize improving graph quality and representation. Specifically, various types of graphs can be derived from naturally structured data, including heterogeneous graphs, hypergraphs, and directed graphs. Among these, directed graphs offer distinct advantages in topological systems by modeling causal relationships, and directed GNNs have been extensively studied in recent years. However, a comprehensive survey of this emerging topic is still lacking. Therefore, we aim to provide a comprehensive review of directed graph learning, with a particular focus on a data-centric perspective. Specifically, we first introduce a novel taxonomy for existing studies. Subsequently, we re-examine these methods from the data-centric perspective, with an emphasis on understanding and improving data representation. It demonstrates that a deep understanding of directed graphs and their quality plays a crucial role in model performance. Additionally, we explore the diverse applications of directed GNNs across 10+ domains, highlighting their broad applicability. Finally, we identify key opportunities and challenges within the field, offering insights that can guide future research and development in directed graph learning.

Many graph algorithms can be viewed as sets of rules that are iteratively applied, with the number of iterations dependent on the size and complexity of the input graph. Existing machine learning architectures often struggle to represent these algorithmic decisions as discrete state transitions. Therefore, we propose a novel framework: GraphFSA (Graph Finite State Automaton). GraphFSA is designed to learn a finite state automaton that runs on each node of a given graph. We test GraphFSA on cellular automata problems, showcasing its abilities in a straightforward algorithmic setting. For a comprehensive empirical evaluation of our framework, we create a diverse range of synthetic problems. As our main application, we then focus on learning more elaborate graph algorithms. Our findings suggest that GraphFSA exhibits strong generalization and extrapolation abilities, presenting an alternative approach to represent these algorithms.

Due to the advantages of hypergraphs in modeling high-order relationships in complex systems, they have been applied to higher-order clustering, hypergraph neural networks and computer vision. These applications rely heavily on access to high-quality, large-scale real-world hypergraph data. Yet, compared to traditional pairwise graphs, real hypergraph datasets remain scarce in both scale and diversity. This shortage significantly limits the development and evaluation of advanced hypergraph learning algorithms. Therefore, how to quickly generate large-scale hypergraphs that conform to the characteristics of real networks is a crucial task that has not received sufficient attention. Motivated by recent advances in large language models (LLMs), particularly their capabilities in semantic reasoning, structured generation, and simulating human behavior, we investigate whether LLMs can facilitate hypergraph generation from a fundamentally new perspective. We introduce HyperLLM, a novel LLM-driven hypergraph generator that simulates the formation and evolution of hypergraphs through a multi-agent collaboration. The framework integrates prompts and structural feedback mechanisms to ensure that the generated hypergraphs reflect key real-world patterns. Extensive experiments across diverse datasets demonstrate that HyperLLM achieves superior fidelity to structural and temporal hypergraph patterns, while requiring minimal statistical priors. Our findings suggest that LLM-based frameworks offer a promising new direction for hypergraph modeling.

Graph-based collaborative filtering methods have prevailing performance for recommender systems since they can capture high-order information between users and items, in which the graphs are constructed from the observed user-item interactions that might miss links or contain spurious positive interactions in industrial scenarios. The Bayesian Graph Neural Network framework approaches this issue with generative models for the interaction graphs. The critical problem is to devise a proper family of graph generative models tailored to recommender systems. We propose an efficient generative model that jointly considers the preferences of users, the concurrence of items and some important graph structure information. Experiments on four popular benchmark datasets demonstrate the effectiveness of our proposed graph generative methods for recommender systems.

Graph Structure Learning (GSL) has recently garnered considerable attention due to its ability to optimize both the parameters of Graph Neural Networks (GNNs) and the computation graph structure simultaneously. Despite the proliferation of GSL methods developed in recent years, there is no standard experimental setting or fair comparison for performance evaluation, which creates a great obstacle to understanding the progress in this field. To fill this gap, we systematically analyze the performance of GSL in different scenarios and develop a comprehensive Graph Structure Learning Benchmark (GSLB) curated from 20 diverse graph datasets and 16 distinct GSL algorithms. Specifically, GSLB systematically investigates the characteristics of GSL in terms of three dimensions: effectiveness, robustness, and complexity. We comprehensively evaluate state-of-the-art GSL algorithms in node- and graph-level tasks, and analyze their performance in robust learning and model complexity. Further, to facilitate reproducible research, we have developed an easy-to-use library for training, evaluating, and visualizing different GSL methods. Empirical results of our extensive experiments demonstrate the ability of GSL and reveal its potential benefits on various downstream tasks, offering insights and opportunities for future research. The code of GSLB is available at: https://github.com/GSL-Benchmark/GSLB.

Graph mining workloads aim to extract structural properties of a graph by exploring its subgraph structures. General purpose graph mining systems provide a generic runtime to explore subgraph structures of interest with the help of user-defined functions that guide the overall exploration process. However, the state-of-the-art graph mining systems remain largely oblivious to the shape (or pattern) of the subgraphs that they mine. This causes them to: (a) explore unnecessary subgraphs; (b) perform expensive computations on the explored subgraphs; and, (c) hold intermediate partial subgraphs in memory; all of which affect their overall performance. Furthermore, their programming models are often tied to their underlying exploration strategies, which makes it difficult for domain users to express complex mining tasks. In this paper, we develop Peregrine, a pattern-aware graph mining system that directly explores the subgraphs of interest while avoiding exploration of unnecessary subgraphs, and simultaneously bypassing expensive computations throughout the mining process. We design a pattern-based programming model that treats "graph patterns" as first class constructs and enables Peregrine to extract the semantics of patterns, which it uses to guide its exploration. Our evaluation shows that Peregrine outperforms state-of-the-art distributed and single machine graph mining systems, and scales to complex mining tasks on larger graphs, while retaining simplicity and expressivity with its "pattern-first" programming approach.

Graph-structured data are the commonly used and have wide application scenarios in the real world. For these diverse applications, the vast variety of learning tasks, graph domains, and complex graph learning procedures present challenges for human experts when designing versatile graph learning approaches. Facing these challenges, large language models (LLMs) offer a potential solution due to the extensive knowledge and the human-like intelligence. This paper proposes a novel conceptual prototype for designing versatile graph learning methods with LLMs, with a particular focus on the "where" and "how" perspectives. From the "where" perspective, we summarize four key graph learning procedures, including task definition, graph data feature engineering, model selection and optimization, deployment and serving. We then explore the application scenarios of LLMs in these procedures across a wider spectrum. In the "how" perspective, we align the abilities of LLMs with the requirements of each procedure. Finally, we point out the promising directions that could better leverage the strength of LLMs towards versatile graph learning methods.

The era of foundation models has revolutionized AI research, yet Graph Foundation Models (GFMs) remain constrained by the scarcity of large-scale graph corpora. Traditional graph data synthesis techniques primarily focus on simplistic structural operations, lacking the capacity to generate semantically rich nodes with meaningful textual attributes: a critical limitation for real-world applications. While large language models (LLMs) demonstrate exceptional text generation capabilities, their direct application to graph synthesis is impeded by context window limitations, hallucination phenomena, and structural consistency challenges. To address these issues, we introduce GraphMaster, the first multi-agent framework specifically designed for graph data synthesis in data-limited environments. GraphMaster orchestrates four specialized LLM agents (Manager, Perception, Enhancement, and Evaluation) that collaboratively optimize the synthesis process through iterative refinement, ensuring both semantic coherence and structural integrity. To rigorously evaluate our approach, we create new data-limited "Sub" variants of six standard graph benchmarks, specifically designed to test synthesis capabilities under realistic constraints. Additionally, we develop a novel interpretability assessment framework that combines human evaluation with a principled Grassmannian manifold-based analysis, providing both qualitative and quantitative measures of semantic coherence. Experimental results demonstrate that GraphMaster significantly outperforms traditional synthesis methods across multiple datasets, establishing a strong foundation for advancing GFMs in data-scarce environments.

Graph measures that express closeness or distance between nodes can be employed for graph nodes clustering using metric clustering algorithms. There are numerous measures applicable to this task, and which one performs better is an open question. We study the performance of 25 graph measures on generated graphs with different parameters. While usually measure comparisons are limited to general measure ranking on a particular dataset, we aim to explore the performance of various measures depending on graph features. Using an LFR graph generator, we create a dataset of 11780 graphs covering the whole LFR parameter space. For each graph, we assess the quality of clustering with k-means algorithm for each considered measure. Based on this, we determine the best measure for each area of the parameter space. We find that the parameter space consists of distinct zones where one particular measure is the best. We analyze the geometry of the resulting zones and describe it with simple criteria. Given particular graph parameters, this allows us to recommend a particular measure to use for clustering.

Foundation models have emerged as critical components in a variety of artificial intelligence applications, and showcase significant success in natural language processing and several other domains. Meanwhile, the field of graph machine learning is witnessing a paradigm transition from shallow methods to more sophisticated deep learning approaches. The capabilities of foundation models to generalize and adapt motivate graph machine learning researchers to discuss the potential of developing a new graph learning paradigm. This paradigm envisions models that are pre-trained on extensive graph data and can be adapted for various graph tasks. Despite this burgeoning interest, there is a noticeable lack of clear definitions and systematic analyses pertaining to this new domain. To this end, this article introduces the concept of Graph Foundation Models (GFMs), and offers an exhaustive explanation of their key characteristics and underlying technologies. We proceed to classify the existing work related to GFMs into three distinct categories, based on their dependence on graph neural networks and large language models. In addition to providing a thorough review of the current state of GFMs, this article also outlooks potential avenues for future research in this rapidly evolving domain.

The arXiv has collected 1.5 million pre-print articles over 28 years, hosting literature from scientific fields including Physics, Mathematics, and Computer Science. Each pre-print features text, figures, authors, citations, categories, and other metadata. These rich, multi-modal features, combined with the natural graph structure---created by citation, affiliation, and co-authorship---makes the arXiv an exciting candidate for benchmarking next-generation models. Here we take the first necessary steps toward this goal, by providing a pipeline which standardizes and simplifies access to the arXiv's publicly available data. We use this pipeline to extract and analyze a 6.7 million edge citation graph, with an 11 billion word corpus of full-text research articles. We present some baseline classification results, and motivate application of more exciting generative graph models.

We introduceGraphGPT, a novel self-supervised generative pre-trained model for graph learning based on the Graph Eulerian Transformer (GET). First, we propose GET, which combines a standard transformer encoder or decoder architecture with an innovative graph-to-sequence transformation method. This method converts graphs or sampled subgraphs into sequences of tokens representing nodes, edges, and attributes in a reversible manner using Eulerian paths. We pre-train GET using either of the two self-supervised tasks: next-token prediction (NTP) and scheduled masked-token prediction (SMTP). The pre-trained model is then fine-tuned for downstream tasks such as graph-, edge-, and node-level prediction. Despite its simplicity, GraphGPT achieves performance comparable to or surpassing state-of-the-art methods on multiple large-scale Open Graph Benchmark (OGB) datasets. It demonstrates exceptional results on the molecular property prediction dataset PCQM4Mv2 and the protein-protein interaction dataset ogbl-ppa. Notably, generative pre-training enables scaling GraphGPT to 2 billion parameters while maintaining performance gains - a breakthrough that overcomes the scalability limitations of traditional Graph Neural Networks (GNNs) and prior graph transformers (GTs). To advance research in graph foundation models and facilitate scientific discovery in chemistry, materials science, and related fields, we will release the source code (https://github.com/alibaba/graph-gpt) and pre-trained checkpoints.

In recent years, graph pre-training has gained significant attention, focusing on acquiring transferable knowledge from unlabeled graph data to improve downstream performance. Despite these recent endeavors, the problem of negative transfer remains a major concern when utilizing graph pre-trained models to downstream tasks. Previous studies made great efforts on the issue of what to pre-train and how to pre-train by designing a variety of graph pre-training and fine-tuning strategies. However, there are cases where even the most advanced "pre-train and fine-tune" paradigms fail to yield distinct benefits. This paper introduces a generic framework W2PGNN to answer the crucial question of when to pre-train (i.e., in what situations could we take advantage of graph pre-training) before performing effortful pre-training or fine-tuning. We start from a new perspective to explore the complex generative mechanisms from the pre-training data to downstream data. In particular, W2PGNN first fits the pre-training data into graphon bases, each element of graphon basis (i.e., a graphon) identifies a fundamental transferable pattern shared by a collection of pre-training graphs. All convex combinations of graphon bases give rise to a generator space, from which graphs generated form the solution space for those downstream data that can benefit from pre-training. In this manner, the feasibility of pre-training can be quantified as the generation probability of the downstream data from any generator in the generator space. W2PGNN offers three broad applications: providing the application scope of graph pre-trained models, quantifying the feasibility of pre-training, and assistance in selecting pre-training data to enhance downstream performance. We provide a theoretically sound solution for the first application and extensive empirical justifications for the latter two applications.

The generation of explanation graphs is a significant task that aims to produce explanation graphs in response to user input, revealing the internal reasoning process. This task is challenging due to the significant discrepancy between unstructured user queries and structured explanation graphs. Current research commonly fine-tunes a text-based pre-trained language model on a small downstream dataset that is annotated with labeled graphs. However, due to the limited scale of available datasets, this approach may prove to be insufficient in bridging the gap between natural language text and structured graphs. In this paper, to alleviate the above limitations, we propose a novel pre-trained framework EG3P(for Explanation Graph Generation via Generative Pre-training over synthetic graphs) for the explanation graph generation task. Specifically, we first propose a text-to-graph generative task to pre-train the model with the goal of bridging the text-graph gap. Additionally, we propose an automatic corpus synthesis strategy for synthesizing a large scale of high-quality corpus, reducing the reliance on costly manual annotation methods. Experimental results on ExplaGraphs show the effectiveness of EG3P that our model surpasses all baseline systems with remarkable margins. Besides, further analysis demonstrates that EG3P is able to generate better explanation graphs on actual reasoning tasks such as CommonsenseQA and OpenbookQA.

Given a massive graph, how can we exploit its hierarchical structure for concisely but exactly summarizing the graph? By exploiting the structure, can we achieve better compression rates than state-of-the-art graph summarization methods? The explosive proliferation of the Web has accelerated the emergence of large graphs, such as online social networks and hyperlink networks. Consequently, graph compression has become increasingly important to process such large graphs without expensive I/O over the network or to disk. Among a number of approaches, graph summarization, which in essence combines similar nodes into a supernode and describe their connectivity concisely, protrudes with several advantages. However, we note that it fails to exploit pervasive hierarchical structures of real-world graphs as its underlying representation model enforces supernodes to be disjoint. In this work, we propose the hierarchical graph summarization model, which is an expressive graph representation model that includes the previous one proposed by Navlakha et al. as a special case. The new model represents an unweighted graph using positive and negative edges between hierarchical supernodes, each of which can contain others. Then, we propose Slugger, a scalable heuristic for concisely and exactly representing a given graph under our new model. Slugger greedily merges nodes into supernodes while maintaining and exploiting their hierarchy, which is later pruned. Slugger significantly accelerates this process by sampling, approximation, and memoization. Our experiments on 16 real-world graphs show that Slugger is (a) Effective: yielding up to 29.6% more concise summary than state-of-the-art lossless summarization methods, (b) Fast: summarizing a graph with 0.8 billion edges in a few hours, and (c) Scalable: scaling linearly with the number of edges in the input graph.

In this paper, we aim to develop a large language model (LLM) with the reasoning ability on complex graph data. Currently, LLMs have achieved very impressive performance on various natural language learning tasks, extensions of which have also been applied to study the vision tasks with multi-modal data. However, when it comes to the graph learning tasks, existing LLMs present very serious flaws due to their several inherited weaknesses in performing {multi-step logic reasoning}, {precise mathematical calculation} and {perception about the spatial and temporal factors}. To address such challenges, in this paper, we will investigate the principles, methodologies and algorithms to empower existing LLMs with graph reasoning ability, which will have tremendous impacts on the current research of both LLMs and graph learning. Inspired by the latest ChatGPT and Toolformer models, we propose the Graph-ToolFormer (Graph Reasoning oriented Toolformer) framework to teach LLMs themselves with prompts augmented by ChatGPT to use external graph reasoning API tools. Specifically, we will investigate to teach Graph-ToolFormer to handle various graph data reasoning tasks in this paper, including both (1) very basic graph data loading and graph property reasoning tasks, ranging from simple graph order and size to the graph diameter and periphery, and (2) more advanced reasoning tasks on real-world graph data, such as bibliographic networks, protein molecules, sequential recommender systems, social networks and knowledge graphs.

Scene graph generation (SGG) aims to predict graph-structured descriptions of input images, in the form of objects and relationships between them. This task is becoming increasingly useful for progress at the interface of vision and language. Here, it is important - yet challenging - to perform well on novel (zero-shot) or rare (few-shot) compositions of objects and relationships. In this paper, we identify two key issues that limit such generalization. Firstly, we show that the standard loss used in this task is unintentionally a function of scene graph density. This leads to the neglect of individual edges in large sparse graphs during training, even though these contain diverse few-shot examples that are important for generalization. Secondly, the frequency of relationships can create a strong bias in this task, such that a blind model predicting the most frequent relationship achieves good performance. Consequently, some state-of-the-art models exploit this bias to improve results. We show that such models can suffer the most in their ability to generalize to rare compositions, evaluating two different models on the Visual Genome dataset and its more recent, improved version, GQA. To address these issues, we introduce a density-normalized edge loss, which provides more than a two-fold improvement in certain generalization metrics. Compared to other works in this direction, our enhancements require only a few lines of code and no added computational cost. We also highlight the difficulty of accurately evaluating models using existing metrics, especially on zero/few shots, and introduce a novel weighted metric.

The growing demand for automated graph algorithm reasoning has attracted increasing attention in the large language model (LLM) community. Recent LLM-based graph reasoning methods typically decouple task descriptions from graph data, generate executable code augmented by retrieval from technical documentation, and refine the code through debugging. However, we identify two key limitations in existing approaches: (i) they treat technical documentation as flat text collections and ignore its hierarchical structure, leading to noisy retrieval that degrades code generation quality; and (ii) their debugging mechanisms focus primarily on runtime errors, yet ignore more critical logical errors. To address them, we propose {\method}, an agentic hierarchical retrieval-augmented coding framework that exploits the document hierarchy through top-down traversal and early pruning, together with a self-debugging coding agent that iteratively refines code using automatically generated small-scale test cases. To enable comprehensive evaluation of complex graph reasoning, we introduce a new dataset, {\dataset}, covering small-scale, large-scale, and composite graph reasoning tasks. Extensive experiments demonstrate that our method achieves higher task accuracy and lower inference cost compared to baselinesThe code is available at \href{https://github.com/FairyFali/GraphSkill{blue{https://github.com/FairyFali/GraphSkill}}.}.

Retrieval-augmented generation (RAG) is a powerful technique that enhances downstream task execution by retrieving additional information, such as knowledge, skills, and tools from external sources. Graph, by its intrinsic "nodes connected by edges" nature, encodes massive heterogeneous and relational information, making it a golden resource for RAG in tremendous real-world applications. As a result, we have recently witnessed increasing attention on equipping RAG with Graph, i.e., GraphRAG. However, unlike conventional RAG, where the retriever, generator, and external data sources can be uniformly designed in the neural-embedding space, the uniqueness of graph-structured data, such as diverse-formatted and domain-specific relational knowledge, poses unique and significant challenges when designing GraphRAG for different domains. Given the broad applicability, the associated design challenges, and the recent surge in GraphRAG, a systematic and up-to-date survey of its key concepts and techniques is urgently desired. Following this motivation, we present a comprehensive and up-to-date survey on GraphRAG. Our survey first proposes a holistic GraphRAG framework by defining its key components, including query processor, retriever, organizer, generator, and data source. Furthermore, recognizing that graphs in different domains exhibit distinct relational patterns and require dedicated designs, we review GraphRAG techniques uniquely tailored to each domain. Finally, we discuss research challenges and brainstorm directions to inspire cross-disciplinary opportunities. Our survey repository is publicly maintained at https://github.com/Graph-RAG/GraphRAG/.

The use of graph neural networks has produced significant advances in point cloud problems, such as those found in high energy physics. The question of how to produce a graph structure in these problems is usually treated as a matter of heuristics, employing fully connected graphs or K-nearest neighbors. In this work, we elevate this question to utmost importance as the Topology Problem. We propose an attention mechanism that allows a graph to be constructed in a learned space that handles geometrically the flow of relevance, providing one solution to the Topology Problem. We test this architecture, called GravNetNorm, on the task of top jet tagging, and show that it is competitive in tagging accuracy, and uses far fewer computational resources than all other comparable models.

Scene graph generation has emerged as a prominent research field in computer vision, witnessing significant advancements in the recent years. However, despite these strides, precise and thorough definitions for the metrics used to evaluate scene graph generation models are lacking. In this paper, we address this gap in the literature by providing a review and precise definition of commonly used metrics in scene graph generation. Our comprehensive examination clarifies the underlying principles of these metrics and can serve as a reference or introduction to scene graph metrics. Furthermore, to facilitate the usage of these metrics, we introduce a standalone Python package called SGBench that efficiently implements all defined metrics, ensuring their accessibility to the research community. Additionally, we present a scene graph benchmarking web service, that enables researchers to compare scene graph generation methods and increase visibility of new methods in a central place. All of our code can be found at https://lorjul.github.io/sgbench/.

We introduce a framework for automatically defining and learning deep generative models with problem-specific structure. We tackle problem domains that are more traditionally solved by algorithms such as sorting, constraint satisfaction for Sudoku, and matrix factorization. Concretely, we train diffusion models with an architecture tailored to the problem specification. This problem specification should contain a graphical model describing relationships between variables, and often benefits from explicit representation of subcomputations. Permutation invariances can also be exploited. Across a diverse set of experiments we improve the scaling relationship between problem dimension and our model's performance, in terms of both training time and final accuracy. Our code can be found at https://github.com/plai-group/gsdm.

Generating explanations for graph neural networks (GNNs) has been studied to understand their behavior in analytical tasks such as graph classification. Existing approaches aim to understand the overall results of GNNs rather than providing explanations for specific class labels of interest, and may return explanation structures that are hard to access, nor directly queryable.We propose GVEX, a novel paradigm that generates Graph Views for EXplanation. (1) We design a two-tier explanation structure called explanation views. An explanation view consists of a set of graph patterns and a set of induced explanation subgraphs. Given a database G of multiple graphs and a specific class label l assigned by a GNN-based classifier M, it concisely describes the fraction of G that best explains why l is assigned by M. (2) We propose quality measures and formulate an optimization problem to compute optimal explanation views for GNN explanation. We show that the problem is Σ^2_P-hard. (3) We present two algorithms. The first one follows an explain-and-summarize strategy that first generates high-quality explanation subgraphs which best explain GNNs in terms of feature influence maximization, and then performs a summarization step to generate patterns. We show that this strategy provides an approximation ratio of 1/2. Our second algorithm performs a single-pass to an input node stream in batches to incrementally maintain explanation views, having an anytime quality guarantee of 1/4 approximation. Using real-world benchmark data, we experimentally demonstrate the effectiveness, efficiency, and scalability of GVEX. Through case studies, we showcase the practical applications of GVEX.

We propose a generalization of transformer neural network architecture for arbitrary graphs. The original transformer was designed for Natural Language Processing (NLP), which operates on fully connected graphs representing all connections between the words in a sequence. Such architecture does not leverage the graph connectivity inductive bias, and can perform poorly when the graph topology is important and has not been encoded into the node features. We introduce a graph transformer with four new properties compared to the standard model. First, the attention mechanism is a function of the neighborhood connectivity for each node in the graph. Second, the positional encoding is represented by the Laplacian eigenvectors, which naturally generalize the sinusoidal positional encodings often used in NLP. Third, the layer normalization is replaced by a batch normalization layer, which provides faster training and better generalization performance. Finally, the architecture is extended to edge feature representation, which can be critical to tasks s.a. chemistry (bond type) or link prediction (entity relationship in knowledge graphs). Numerical experiments on a graph benchmark demonstrate the performance of the proposed graph transformer architecture. This work closes the gap between the original transformer, which was designed for the limited case of line graphs, and graph neural networks, that can work with arbitrary graphs. As our architecture is simple and generic, we believe it can be used as a black box for future applications that wish to consider transformer and graphs.

This work presents a graph neural network (GNN) framework for solving the maximum independent set (MIS) problem, inspired by dynamic programming (DP). Specifically, given a graph, we propose a DP-like recursive algorithm based on GNNs that firstly constructs two smaller sub-graphs, predicts the one with the larger MIS, and then uses it in the next recursive call. To train our algorithm, we require annotated comparisons of different graphs concerning their MIS size. Annotating the comparisons with the output of our algorithm leads to a self-training process that results in more accurate self-annotation of the comparisons and vice versa. We provide numerical evidence showing the superiority of our method vs prior methods in multiple synthetic and real-world datasets.

Low-dimensional embeddings of nodes in large graphs have proved extremely useful in a variety of prediction tasks, from content recommendation to identifying protein functions. However, most existing approaches require that all nodes in the graph are present during training of the embeddings; these previous approaches are inherently transductive and do not naturally generalize to unseen nodes. Here we present GraphSAGE, a general, inductive framework that leverages node feature information (e.g., text attributes) to efficiently generate node embeddings for previously unseen data. Instead of training individual embeddings for each node, we learn a function that generates embeddings by sampling and aggregating features from a node's local neighborhood. Our algorithm outperforms strong baselines on three inductive node-classification benchmarks: we classify the category of unseen nodes in evolving information graphs based on citation and Reddit post data, and we show that our algorithm generalizes to completely unseen graphs using a multi-graph dataset of protein-protein interactions.

Graph neural networks achieve high accuracy in link prediction by jointly leveraging graph topology and node attributes. Topology, however, is represented indirectly; state-of-the-art methods based on subgraph classification label nodes with distance to the target link, so that, although topological information is present, it is tempered by pooling. This makes it challenging to leverage features like loops and motifs associated with network formation mechanisms. We propose a link prediction algorithm based on a new pooling scheme called WalkPool. WalkPool combines the expressivity of topological heuristics with the feature-learning ability of neural networks. It summarizes a putative link by random walk probabilities of adjacent paths. Instead of extracting transition probabilities from the original graph, it computes the transition matrix of a "predictive" latent graph by applying attention to learned features; this may be interpreted as feature-sensitive topology fingerprinting. WalkPool can leverage unsupervised node features or be combined with GNNs and trained end-to-end. It outperforms state-of-the-art methods on all common link prediction benchmarks, both homophilic and heterophilic, with and without node attributes. Applying WalkPool to a set of unsupervised GNNs significantly improves prediction accuracy, suggesting that it may be used as a general-purpose graph pooling scheme.

Graph neural networks have recently achieved remarkable success in representing graph-structured data, with rapid progress in both the node embedding and graph pooling methods. Yet, they mostly focus on capturing information from the nodes considering their connectivity, and not much work has been done in representing the edges, which are essential components of a graph. However, for tasks such as graph reconstruction and generation, as well as graph classification tasks for which the edges are important for discrimination, accurately representing edges of a given graph is crucial to the success of the graph representation learning. To this end, we propose a novel edge representation learning framework based on Dual Hypergraph Transformation (DHT), which transforms the edges of a graph into the nodes of a hypergraph. This dual hypergraph construction allows us to apply message-passing techniques for node representations to edges. After obtaining edge representations from the hypergraphs, we then cluster or drop edges to obtain holistic graph-level edge representations. We validate our edge representation learning method with hypergraphs on diverse graph datasets for graph representation and generation performance, on which our method largely outperforms existing graph representation learning methods. Moreover, our edge representation learning and pooling method also largely outperforms state-of-the-art graph pooling methods on graph classification, not only because of its accurate edge representation learning, but also due to its lossless compression of the nodes and removal of irrelevant edges for effective message-passing.

Graphs are a powerful tool for representing and analyzing complex relationships in real-world applications such as social networks, recommender systems, and computational finance. Reasoning on graphs is essential for drawing inferences about the relationships between entities in a complex system, and to identify hidden patterns and trends. Despite the remarkable progress in automated reasoning with natural text, reasoning on graphs with large language models (LLMs) remains an understudied problem. In this work, we perform the first comprehensive study of encoding graph-structured data as text for consumption by LLMs. We show that LLM performance on graph reasoning tasks varies on three fundamental levels: (1) the graph encoding method, (2) the nature of the graph task itself, and (3) interestingly, the very structure of the graph considered. These novel results provide valuable insight on strategies for encoding graphs as text. Using these insights we illustrate how the correct choice of encoders can boost performance on graph reasoning tasks inside LLMs by 4.8% to 61.8%, depending on the task.

Standard Retrieval-Augmented Generation (RAG) relies on chunk-based retrieval, whereas GraphRAG advances this approach by graph-based knowledge representation. However, existing graph-based RAG approaches are constrained by binary relations, as each edge in an ordinary graph connects only two entities, limiting their ability to represent the n-ary relations (n >= 2) in real-world knowledge. In this work, we propose HyperGraphRAG, a novel hypergraph-based RAG method that represents n-ary relational facts via hyperedges, and consists of knowledge hypergraph construction, retrieval, and generation. Experiments across medicine, agriculture, computer science, and law demonstrate that HyperGraphRAG outperforms both standard RAG and previous graph-based RAG methods in answer accuracy, retrieval efficiency, and generation quality.

Graph neural networks are popular architectures for graph machine learning, based on iterative computation of node representations of an input graph through a series of invariant transformations. A large class of graph neural networks follow a standard message-passing paradigm: at every layer, each node state is updated based on an aggregate of messages from its neighborhood. In this work, we propose a novel framework for training graph neural networks, where every node is viewed as a player that can choose to either 'listen', 'broadcast', 'listen and broadcast', or to 'isolate'. The standard message propagation scheme can then be viewed as a special case of this framework where every node 'listens and broadcasts' to all neighbors. Our approach offers a more flexible and dynamic message-passing paradigm, where each node can determine its own strategy based on their state, effectively exploring the graph topology while learning. We provide a theoretical analysis of the new message-passing scheme which is further supported by an extensive empirical analysis on a synthetic dataset and on real-world datasets.

Can we model non-Euclidean graphs as pure language or even Euclidean vectors while retaining their inherent information? The non-Euclidean property have posed a long term challenge in graph modeling. Despite recent GNN and Graphformer efforts encoding graphs as Euclidean vectors, recovering original graph from the vectors remains a challenge. We introduce GraphsGPT, featuring a Graph2Seq encoder that transforms non-Euclidean graphs into learnable graph words in a Euclidean space, along with a GraphGPT decoder that reconstructs the original graph from graph words to ensure information equivalence. We pretrain GraphsGPT on 100M molecules and yield some interesting findings: (1) Pretrained Graph2Seq excels in graph representation learning, achieving state-of-the-art results on 8/9 graph classification and regression tasks. (2) Pretrained GraphGPT serves as a strong graph generator, demonstrated by its ability to perform both unconditional and conditional graph generation. (3) Graph2Seq+GraphGPT enables effective graph mixup in the Euclidean space, overcoming previously known non-Euclidean challenge. (4) Our proposed novel edge-centric GPT pretraining task is effective in graph fields, underscoring its success in both representation and generation.

We study a new connection between a technical measure called mu-conductance that arises in the study of Markov chains for sampling convex bodies and the network community profile that characterizes size-resolved properties of clusters and communities in social and information networks. The idea of mu-conductance is similar to the traditional graph conductance, but disregards sets with small volume. We derive a sequence of optimization problems including a low-rank semi-definite program from which we can derive a lower bound on the optimal mu-conductance value. These ideas give the first theoretically sound bound on the behavior of the network community profile for a wide range of cluster sizes. The algorithm scales up to graphs with hundreds of thousands of nodes and we demonstrate how our framework validates the predicted structures of real-world graphs.

Artificial General Intelligence (AGI) has revolutionized numerous fields, yet its integration with graph data, a cornerstone in our interconnected world, remains nascent. This paper presents a pioneering survey on the emerging domain of graph prompts in AGI, addressing key challenges and opportunities in harnessing graph data for AGI applications. Despite substantial advancements in AGI across natural language processing and computer vision, the application to graph data is relatively underexplored. This survey critically evaluates the current landscape of AGI in handling graph data, highlighting the distinct challenges in cross-modality, cross-domain, and cross-task applications specific to graphs. Our work is the first to propose a unified framework for understanding graph prompt learning, offering clarity on prompt tokens, token structures, and insertion patterns in the graph domain. We delve into the intrinsic properties of graph prompts, exploring their flexibility, expressiveness, and interplay with existing graph models. A comprehensive taxonomy categorizes over 100 works in this field, aligning them with pre-training tasks across node-level, edge-level, and graph-level objectives. Additionally, we present, ProG, a Python library, and an accompanying website, to support and advance research in graph prompting. The survey culminates in a discussion of current challenges and future directions, offering a roadmap for research in graph prompting within AGI. Through this comprehensive analysis, we aim to catalyze further exploration and practical applications of AGI in graph data, underlining its potential to reshape AGI fields and beyond. ProG and the website can be accessed by https://github.com/WxxShirley/Awesome-Graph-Prompt, and https://github.com/sheldonresearch/ProG, respectively.

Graph convolutional networks (GCNs) enable end-to-end learning on graph structured data. However, many works assume a given graph structure. When the input graph is noisy or unavailable, one approach is to construct or learn a latent graph structure. These methods typically fix the choice of node degree for the entire graph, which is suboptimal. Instead, we propose a novel end-to-end differentiable graph generator which builds graph topologies where each node selects both its neighborhood and its size. Our module can be readily integrated into existing pipelines involving graph convolution operations, replacing the predetermined or existing adjacency matrix with one that is learned, and optimized, as part of the general objective. As such it is applicable to any GCN. We integrate our module into trajectory prediction, point cloud classification and node classification pipelines resulting in improved accuracy over other structure-learning methods across a wide range of datasets and GCN backbones.

Recently, Retrieval-Augmented Generation (RAG) has achieved remarkable success in addressing the challenges of Large Language Models (LLMs) without necessitating retraining. By referencing an external knowledge base, RAG refines LLM outputs, effectively mitigating issues such as ``hallucination'', lack of domain-specific knowledge, and outdated information. However, the complex structure of relationships among different entities in databases presents challenges for RAG systems. In response, GraphRAG leverages structural information across entities to enable more precise and comprehensive retrieval, capturing relational knowledge and facilitating more accurate, context-aware responses. Given the novelty and potential of GraphRAG, a systematic review of current technologies is imperative. This paper provides the first comprehensive overview of GraphRAG methodologies. We formalize the GraphRAG workflow, encompassing Graph-Based Indexing, Graph-Guided Retrieval, and Graph-Enhanced Generation. We then outline the core technologies and training methods at each stage. Additionally, we examine downstream tasks, application domains, evaluation methodologies, and industrial use cases of GraphRAG. Finally, we explore future research directions to inspire further inquiries and advance progress in the field.

Graph Neural Networks (GNNs) are a powerful tool for machine learning on graphs.GNNs combine node feature information with the graph structure by recursively passing neural messages along edges of the input graph. However, incorporating both graph structure and feature information leads to complex models, and explaining predictions made by GNNs remains unsolved. Here we propose GNNExplainer, the first general, model-agnostic approach for providing interpretable explanations for predictions of any GNN-based model on any graph-based machine learning task. Given an instance, GNNExplainer identifies a compact subgraph structure and a small subset of node features that have a crucial role in GNN's prediction. Further, GNNExplainer can generate consistent and concise explanations for an entire class of instances. We formulate GNNExplainer as an optimization task that maximizes the mutual information between a GNN's prediction and distribution of possible subgraph structures. Experiments on synthetic and real-world graphs show that our approach can identify important graph structures as well as node features, and outperforms baselines by 17.1% on average. GNNExplainer provides a variety of benefits, from the ability to visualize semantically relevant structures to interpretability, to giving insights into errors of faulty GNNs.

Although there exist several libraries for deep learning on graphs, they are aiming at implementing basic operations for graph deep learning. In the research community, implementing and benchmarking various advanced tasks are still painful and time-consuming with existing libraries. To facilitate graph deep learning research, we introduce DIG: Dive into Graphs, a turnkey library that provides a unified testbed for higher level, research-oriented graph deep learning tasks. Currently, we consider graph generation, self-supervised learning on graphs, explainability of graph neural networks, and deep learning on 3D graphs. For each direction, we provide unified implementations of data interfaces, common algorithms, and evaluation metrics. Altogether, DIG is an extensible, open-source, and turnkey library for researchers to develop new methods and effortlessly compare with common baselines using widely used datasets and evaluation metrics. Source code is available at https://github.com/divelab/DIG.

Graph representation learning resurges as a trending research subject owing to the widespread use of deep learning for Euclidean data, which inspire various creative designs of neural networks in the non-Euclidean domain, particularly graphs. With the success of these graph neural networks (GNN) in the static setting, we approach further practical scenarios where the graph dynamically evolves. Existing approaches typically resort to node embeddings and use a recurrent neural network (RNN, broadly speaking) to regulate the embeddings and learn the temporal dynamics. These methods require the knowledge of a node in the full time span (including both training and testing) and are less applicable to the frequent change of the node set. In some extreme scenarios, the node sets at different time steps may completely differ. To resolve this challenge, we propose EvolveGCN, which adapts the graph convolutional network (GCN) model along the temporal dimension without resorting to node embeddings. The proposed approach captures the dynamism of the graph sequence through using an RNN to evolve the GCN parameters. Two architectures are considered for the parameter evolution. We evaluate the proposed approach on tasks including link prediction, edge classification, and node classification. The experimental results indicate a generally higher performance of EvolveGCN compared with related approaches. The code is available at https://github.com/IBM/EvolveGCN.

GraphRAG enhances large language models (LLMs) to generate quality answers for user questions by retrieving related facts from external knowledge graphs. Existing GraphRAG methods adopt a fixed graph traversal strategy for fact retrieval but we observe that user questions come in different types and require different graph traversal strategies. As such, existing GraphRAG methods are limited in effectiveness (i.e., quality of the generated answers) and/or efficiency (i.e., response time or the number of used tokens). In this paper, we propose to classify the questions according to a complete four-class taxonomy and adaptively select the appropriate graph traversal strategy for each type of questions. Our system PolyG is essentially a query planner for GraphRAG and can handle diverse questions with an unified interface and execution engine. Compared with SOTA GraphRAG methods, PolyG achieves an overall win rate of 75% on generation quality and a speedup up to 4x on response time.

Diffusion models based on permutation-equivariant networks can learn permutation-invariant distributions for graph data. However, in comparison to their non-invariant counterparts, we have found that these invariant models encounter greater learning challenges since 1) their effective target distributions exhibit more modes; 2) their optimal one-step denoising scores are the score functions of Gaussian mixtures with more components. Motivated by this analysis, we propose a non-invariant diffusion model, called SwinGNN, which employs an efficient edge-to-edge 2-WL message passing network and utilizes shifted window based self-attention inspired by SwinTransformers. Further, through systematic ablations, we identify several critical training and sampling techniques that significantly improve the sample quality of graph generation. At last, we introduce a simple post-processing trick, i.e., randomly permuting the generated graphs, which provably converts any graph generative model to a permutation-invariant one. Extensive experiments on synthetic and real-world protein and molecule datasets show that our SwinGNN achieves state-of-the-art performances. Our code is released at https://github.com/qiyan98/SwinGNN.

Aiming at better representing multivariate relationships, this paper investigates a motif dimensional framework for higher-order graph learning. The graph learning effectiveness can be improved through OFFER. The proposed framework mainly aims at accelerating and improving higher-order graph learning results. We apply the acceleration procedure from the dimensional of network motifs. Specifically, the refined degree for nodes and edges are conducted in two stages: (1) employ motif degree of nodes to refine the adjacency matrix of the network; and (2) employ motif degree of edges to refine the transition probability matrix in the learning process. In order to assess the efficiency of the proposed framework, four popular network representation algorithms are modified and examined. By evaluating the performance of OFFER, both link prediction results and clustering results demonstrate that the graph representation learning algorithms enhanced with OFFER consistently outperform the original algorithms with higher efficiency.

Graph Neural Networks (GNNs) have been widely applied to different tasks such as bioinformatics, drug design, and social networks. However, recent studies have shown that GNNs are vulnerable to adversarial attacks which aim to mislead the node or subgraph classification prediction by adding subtle perturbations. Detecting these attacks is challenging due to the small magnitude of perturbation and the discrete nature of graph data. In this paper, we propose a general adversarial edge detection pipeline EDoG without requiring knowledge of the attack strategies based on graph generation. Specifically, we propose a novel graph generation approach combined with link prediction to detect suspicious adversarial edges. To effectively train the graph generative model, we sample several sub-graphs from the given graph data. We show that since the number of adversarial edges is usually low in practice, with low probability the sampled sub-graphs will contain adversarial edges based on the union bound. In addition, considering the strong attacks which perturb a large number of edges, we propose a set of novel features to perform outlier detection as the preprocessing for our detection. Extensive experimental results on three real-world graph datasets including a private transaction rule dataset from a major company and two types of synthetic graphs with controlled properties show that EDoG can achieve above 0.8 AUC against four state-of-the-art unseen attack strategies without requiring any knowledge about the attack type; and around 0.85 with knowledge of the attack type. EDoG significantly outperforms traditional malicious edge detection baselines. We also show that an adaptive attack with full knowledge of our detection pipeline is difficult to bypass it.

The growing importance of understanding and addressing algorithmic bias in artificial intelligence (AI) has led to a surge in research on AI fairness, which often assumes that the underlying data is independent and identically distributed (IID). However, real-world data frequently exists in non-IID graph structures that capture connections among individual units. To effectively mitigate bias in AI systems, it is essential to bridge the gap between traditional fairness literature, designed for IID data, and the prevalence of non-IID graph data. This survey reviews recent advancements in fairness amidst non-IID graph data, including the newly introduced fair graph generation and the commonly studied fair graph classification. In addition, available datasets and evaluation metrics for future research are identified, the limitations of existing work are highlighted, and promising future directions are proposed.

Deep learning has revolutionized many machine learning tasks in recent years, ranging from image classification and video processing to speech recognition and natural language understanding. The data in these tasks are typically represented in the Euclidean space. However, there is an increasing number of applications where data are generated from non-Euclidean domains and are represented as graphs with complex relationships and interdependency between objects. The complexity of graph data has imposed significant challenges on existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph data have emerged. In this survey, we provide a comprehensive overview of graph neural networks (GNNs) in data mining and machine learning fields. We propose a new taxonomy to divide the state-of-the-art graph neural networks into four categories, namely recurrent graph neural networks, convolutional graph neural networks, graph autoencoders, and spatial-temporal graph neural networks. We further discuss the applications of graph neural networks across various domains and summarize the open source codes, benchmark data sets, and model evaluation of graph neural networks. Finally, we propose potential research directions in this rapidly growing field.

Machine learning on graphs has been extensively studied in both academic and industry. However, as the literature on graph learning booms with a vast number of emerging methods and techniques, it becomes increasingly difficult to manually design the optimal machine learning algorithm for different graph-related tasks. To solve this critical challenge, automated machine learning (AutoML) on graphs which combines the strength of graph machine learning and AutoML together, is gaining attention from the research community. Therefore, we comprehensively survey AutoML on graphs in this paper, primarily focusing on hyper-parameter optimization (HPO) and neural architecture search (NAS) for graph machine learning. We further overview libraries related to automated graph machine learning and in-depth discuss AutoGL, the first dedicated open-source library for AutoML on graphs. In the end, we share our insights on future research directions for automated graph machine learning. This paper is the first systematic and comprehensive review of automated machine learning on graphs to the best of our knowledge.

Large Language Models (LLMs) have demonstrated exceptional abilities in reasoning for task planning. However, challenges remain under-explored for parallel schedules. This paper introduces a novel paradigm, plan-over-graph, in which the model first decomposes a real-life textual task into executable subtasks and constructs an abstract task graph. The model then understands this task graph as input and generates a plan for parallel execution. To enhance the planning capability of complex, scalable graphs, we design an automated and controllable pipeline to generate synthetic graphs and propose a two-stage training scheme. Experimental results show that our plan-over-graph method significantly improves task performance on both API-based LLMs and trainable open-sourced LLMs. By normalizing complex tasks as graphs, our method naturally supports parallel execution, demonstrating global efficiency. The code and data are available at https://github.com/zsq259/Plan-over-Graph.

This work explores the problem of generating task graphs of real-world activities. Different from prior formulations, we consider a setting where text transcripts of instructional videos performing a real-world activity (e.g., making coffee) are provided and the goal is to identify the key steps relevant to the task as well as the dependency relationship between these key steps. We propose a novel task graph generation approach that combines the reasoning capabilities of instruction-tuned language models along with clustering and ranking components to generate accurate task graphs in a completely unsupervised manner. We show that the proposed approach generates more accurate task graphs compared to a supervised learning approach on tasks from the ProceL and CrossTask datasets.

The need to analyze graphs is ubiquitous across various fields, from social networks to biological research and recommendation systems. Therefore, enabling the ability of large language models (LLMs) to process graphs is an important step toward more advanced general intelligence. However, current LLM benchmarks on graph analysis require models to directly reason over the prompts describing graph topology, and are thus limited to small graphs with only a few dozens of nodes. In contrast, human experts typically write programs based on popular libraries for task solving, and can thus handle graphs with different scales. To this end, a question naturally arises: can LLMs analyze graphs like professionals? In this paper, we introduce ProGraph, a manually crafted benchmark containing 3 categories of graph tasks. The benchmark expects solutions based on programming instead of directly reasoning over raw inputs. Our findings reveal that the performance of current LLMs is unsatisfactory, with the best model achieving only 36% accuracy. To bridge this gap, we propose LLM4Graph datasets, which include crawled documents and auto-generated codes based on 6 widely used graph libraries. By augmenting closed-source LLMs with document retrieval and fine-tuning open-source ones on the codes, we show 11-32% absolute improvements in their accuracies. Our results underscore that the capabilities of LLMs in handling structured data are still under-explored, and show the effectiveness of LLM4Graph in enhancing LLMs' proficiency of graph analysis. The benchmark, datasets and enhanced open-source models are available at https://github.com/BUPT-GAMMA/ProGraph.

Link prediction is a very fundamental task on graphs. Inspired by traditional path-based methods, in this paper we propose a general and flexible representation learning framework based on paths for link prediction. Specifically, we define the representation of a pair of nodes as the generalized sum of all path representations, with each path representation as the generalized product of the edge representations in the path. Motivated by the Bellman-Ford algorithm for solving the shortest path problem, we show that the proposed path formulation can be efficiently solved by the generalized Bellman-Ford algorithm. To further improve the capacity of the path formulation, we propose the Neural Bellman-Ford Network (NBFNet), a general graph neural network framework that solves the path formulation with learned operators in the generalized Bellman-Ford algorithm. The NBFNet parameterizes the generalized Bellman-Ford algorithm with 3 neural components, namely INDICATOR, MESSAGE and AGGREGATE functions, which corresponds to the boundary condition, multiplication operator, and summation operator respectively. The NBFNet is very general, covers many traditional path-based methods, and can be applied to both homogeneous graphs and multi-relational graphs (e.g., knowledge graphs) in both transductive and inductive settings. Experiments on both homogeneous graphs and knowledge graphs show that the proposed NBFNet outperforms existing methods by a large margin in both transductive and inductive settings, achieving new state-of-the-art results.

We propose a recipe on how to build a general, powerful, scalable (GPS) graph Transformer with linear complexity and state-of-the-art results on a diverse set of benchmarks. Graph Transformers (GTs) have gained popularity in the field of graph representation learning with a variety of recent publications but they lack a common foundation about what constitutes a good positional or structural encoding, and what differentiates them. In this paper, we summarize the different types of encodings with a clearer definition and categorize them as being local, global or relative. The prior GTs are constrained to small graphs with a few hundred nodes, here we propose the first architecture with a complexity linear in the number of nodes and edges O(N+E) by decoupling the local real-edge aggregation from the fully-connected Transformer. We argue that this decoupling does not negatively affect the expressivity, with our architecture being a universal function approximator on graphs. Our GPS recipe consists of choosing 3 main ingredients: (i) positional/structural encoding, (ii) local message-passing mechanism, and (iii) global attention mechanism. We provide a modular framework GraphGPS that supports multiple types of encodings and that provides efficiency and scalability both in small and large graphs. We test our architecture on 16 benchmarks and show highly competitive results in all of them, show-casing the empirical benefits gained by the modularity and the combination of different strategies.

Subgraph matching is vital in knowledge graph (KG) question answering, molecule design, scene graph, code and circuit search, etc. Neural methods have shown promising results for subgraph matching. Our study of recent systems suggests refactoring them into a unified design space for graph matching networks. Existing methods occupy only a few isolated patches in this space, which remains largely uncharted. We undertake the first comprehensive exploration of this space, featuring such axes as attention-based vs. soft permutation-based interaction between query and corpus graphs, aligning nodes vs. edges, and the form of the final scoring network that integrates neural representations of the graphs. Our extensive experiments reveal that judicious and hitherto-unexplored combinations of choices in this space lead to large performance benefits. Beyond better performance, our study uncovers valuable insights and establishes general design principles for neural graph representation and interaction, which may be of wider interest.

Graph clustering, which aims to divide a graph into several homogeneous groups, is a critical area of study with applications that span various fields such as social network analysis, bioinformatics, and image segmentation. This paper explores both traditional and more recent approaches to graph clustering. Firstly, key concepts and definitions in graph theory are introduced. The background section covers essential topics, including graph Laplacians and the integration of Deep Learning in graph analysis. The paper then delves into traditional clustering methods, including Spectral Clustering and the Leiden algorithm. Following this, state-of-the-art clustering techniques that leverage deep learning are examined. A comprehensive comparison of these methods is made through experiments. The paper concludes with a discussion of the practical applications of graph clustering and potential future research directions.

Diffusion models have established themselves as state-of-the-art generative models across various data modalities, including images and videos, due to their ability to accurately approximate complex data distributions. Unlike traditional generative approaches such as VAEs and GANs, diffusion models employ a progressive denoising process that transforms noise into meaningful data over multiple iterative steps. This gradual approach enhances their expressiveness and generation quality. Not only that, diffusion models have also been shown to extract meaningful representations from data while learning to generate samples. Despite their success, the application of diffusion models to graph-structured data remains relatively unexplored, primarily due to the discrete nature of graphs, which necessitates discrete diffusion processes distinct from the continuous methods used in other domains. In this work, we leverage the representational capabilities of diffusion models to learn meaningful embeddings for graph data. By training a discrete diffusion model within an autoencoder framework, we enable both effective autoencoding and representation learning tailored to the unique characteristics of graph-structured data. We only need the encoder at the end to extract representations. Our approach demonstrates the potential of discrete diffusion models to be used for graph representation learning.

Personalized PageRank (PPR) has enormous applications, such as link prediction and recommendation systems for social networks, which often require the fully PPR to be known. Besides, most of real-life graphs are edge-weighted, e.g., the interaction between users on the Facebook network. However, it is computationally difficult to compute the fully PPR, especially on large graphs, not to mention that most existing approaches do not consider the weights of edges. In particular, the existing approach cannot handle graphs with billion edges on a moderate-size cluster. To address this problem, this paper presents a novel study on the computation of fully edge-weighted PPR on large graphs using the distributed computing framework. Specifically, we employ the Monte Carlo approximation that performs a large number of random walks from each node of the graph, and exploits the parallel pipeline framework to reduce the overall running time of the fully PPR. Based on that, we develop several optimization techniques which (i) alleviate the issue of large nodes that could explode the memory space, (ii) pre-compute short walks for small nodes that largely speedup the computation of random walks, and (iii) optimize the amount of random walks to compute in each pipeline that significantly reduces the overhead. With extensive experiments on a variety of real-life graph datasets, we demonstrate that our solution is several orders of magnitude faster than the state-of-the-arts, and meanwhile, largely outperforms the baseline algorithms in terms of accuracy.

Recent advances in representation learning on graphs, mainly leveraging graph convolutional networks, have brought a substantial improvement on many graph-based benchmark tasks. While novel approaches to learning node embeddings are highly suitable for node classification and link prediction, their application to graph classification (predicting a single label for the entire graph) remains mostly rudimentary, typically using a single global pooling step to aggregate node features or a hand-designed, fixed heuristic for hierarchical coarsening of the graph structure. An important step towards ameliorating this is differentiable graph coarsening---the ability to reduce the size of the graph in an adaptive, data-dependent manner within a graph neural network pipeline, analogous to image downsampling within CNNs. However, the previous prominent approach to pooling has quadratic memory requirements during training and is therefore not scalable to large graphs. Here we combine several recent advances in graph neural network design to demonstrate that competitive hierarchical graph classification results are possible without sacrificing sparsity. Our results are verified on several established graph classification benchmarks, and highlight an important direction for future research in graph-based neural networks.

We consider the problem of graph matching, or learning vertex correspondence, between two correlated stochastic block models (SBMs). The graph matching problem arises in various fields, including computer vision, natural language processing and bioinformatics, and in particular, matching graphs with inherent community structure has significance related to de-anonymization of correlated social networks. Compared to the correlated Erdos-Renyi (ER) model, where various efficient algorithms have been developed, among which a few algorithms have been proven to achieve the exact matching with constant edge correlation, no low-order polynomial algorithm has been known to achieve exact matching for the correlated SBMs with constant correlation. In this work, we propose an efficient algorithm for matching graphs with community structure, based on the comparison between partition trees rooted from each vertex, by extending the idea of Mao et al. (2021) to graphs with communities. The partition tree divides the large neighborhoods of each vertex into disjoint subsets using their edge statistics to different communities. Our algorithm is the first low-order polynomial-time algorithm achieving exact matching between two correlated SBMs with high probability in dense graphs.

Graph Retrieval Augmented Generation (GraphRAG) effectively enhances external knowledge integration capabilities by explicitly modeling knowledge relationships, thereby improving the factual accuracy and generation quality of Large Language Models (LLMs) in specialized domains. However, existing methods suffer from two inherent limitations: 1) Inefficient Information Aggregation: They rely on a single agent and fixed iterative patterns, making it difficult to adaptively capture multi-level textual, structural, and degree information within graph data. 2) Rigid Reasoning Mechanism: They employ preset reasoning schemes, which cannot dynamically adjust reasoning depth nor achieve precise semantic correction. To overcome these limitations, we propose Graph Counselor, an GraphRAG method based on multi-agent collaboration. This method uses the Adaptive Graph Information Extraction Module (AGIEM), where Planning, Thought, and Execution Agents work together to precisely model complex graph structures and dynamically adjust information extraction strategies, addressing the challenges of multi-level dependency modeling and adaptive reasoning depth. Additionally, the Self-Reflection with Multiple Perspectives (SR) module improves the accuracy and semantic consistency of reasoning results through self-reflection and backward reasoning mechanisms. Experiments demonstrate that Graph Counselor outperforms existing methods in multiple graph reasoning tasks, exhibiting higher reasoning accuracy and generalization ability. Our code is available at https://github.com/gjq100/Graph-Counselor.git.

Graphs are ubiquitous structures found in numerous real-world applications, such as drug discovery, recommender systems, and social network analysis. To model graph-structured data, graph neural networks (GNNs) have become a popular tool. However, existing GNN architectures encounter challenges in cross-graph learning where multiple graphs have different feature spaces. To address this, recent approaches introduce text-attributed graphs (TAGs), where each node is associated with a textual description, which can be projected into a unified feature space using textual encoders. While promising, this method relies heavily on the availability of text-attributed graph data, which is difficult to obtain in practice. To bridge this gap, we propose a novel method named Topology-Aware Node description Synthesis (TANS), leveraging large language models (LLMs) to convert existing graphs into text-attributed graphs. The key idea is to integrate topological information into LLMs to explain how graph topology influences node semantics. We evaluate our TANS on text-rich, text-limited, and text-free graphs, demonstrating its applicability. Notably, on text-free graphs, our method significantly outperforms existing approaches that manually design node features, showcasing the potential of LLMs for preprocessing graph-structured data in the absence of textual information. The code and data are available at https://github.com/Zehong-Wang/TANS.

Graphic design is essential for visual communication with layouts being fundamental to composing attractive designs. Layout generation differs from pixel-level image synthesis and is unique in terms of the requirement of mutual relations among the desired components. We propose a method for design layout generation that can satisfy user-specified constraints. The proposed neural design network (NDN) consists of three modules. The first module predicts a graph with complete relations from a graph with user-specified relations. The second module generates a layout from the predicted graph. Finally, the third module fine-tunes the predicted layout. Quantitative and qualitative experiments demonstrate that the generated layouts are visually similar to real design layouts. We also construct real designs based on predicted layouts for a better understanding of the visual quality. Finally, we demonstrate a practical application on layout recommendation.

Graph Neural Networks (GNNs) are an effective framework for representation learning of graphs. GNNs follow a neighborhood aggregation scheme, where the representation vector of a node is computed by recursively aggregating and transforming representation vectors of its neighboring nodes. Many GNN variants have been proposed and have achieved state-of-the-art results on both node and graph classification tasks. However, despite GNNs revolutionizing graph representation learning, there is limited understanding of their representational properties and limitations. Here, we present a theoretical framework for analyzing the expressive power of GNNs to capture different graph structures. Our results characterize the discriminative power of popular GNN variants, such as Graph Convolutional Networks and GraphSAGE, and show that they cannot learn to distinguish certain simple graph structures. We then develop a simple architecture that is provably the most expressive among the class of GNNs and is as powerful as the Weisfeiler-Lehman graph isomorphism test. We empirically validate our theoretical findings on a number of graph classification benchmarks, and demonstrate that our model achieves state-of-the-art performance.

We investigate novel random graph embeddings that can be computed in expected polynomial time and that are able to distinguish all non-isomorphic graphs in expectation. Previous graph embeddings have limited expressiveness and either cannot distinguish all graphs or cannot be computed efficiently for every graph. To be able to approximate arbitrary functions on graphs, we are interested in efficient alternatives that become arbitrarily expressive with increasing resources. Our approach is based on Lov\'asz' characterisation of graph isomorphism through an infinite dimensional vector of homomorphism counts. Our empirical evaluation shows competitive results on several benchmark graph learning tasks.

Graph pooling compresses graph information into a compact representation. State-of-the-art graph pooling methods follow a hierarchical approach, which reduces the graph size step-by-step. These methods must balance memory efficiency with preserving node information, depending on whether they use node dropping or node clustering. Additionally, fixed pooling ratios or numbers of pooling layers are predefined for all graphs, which prevents personalized pooling structures from being captured for each individual graph. In this work, inspired by bottom-up grammar induction, we propose an efficient graph parsing algorithm to infer the pooling structure, which then drives graph pooling. The resulting Graph Parsing Network (GPN) adaptively learns personalized pooling structure for each individual graph. GPN benefits from the discrete assignments generated by the graph parsing algorithm, allowing good memory efficiency while preserving node information intact. Experimental results on standard benchmarks demonstrate that GPN outperforms state-of-the-art graph pooling methods in graph classification tasks while being able to achieve competitive performance in node classification tasks. We also conduct a graph reconstruction task to show GPN's ability to preserve node information and measure both memory and time efficiency through relevant tests.

Graphs are widely used for modeling relational data in real-world scenarios, such as social networks and urban computing. Existing LLM-based graph analysis approaches either integrate graph neural networks (GNNs) for specific machine learning tasks, limiting their transferability, or rely solely on LLMs' internal reasoning ability, resulting in suboptimal performance. To address these limitations, we take advantage of recent advances in LLM-based agents, which have shown capabilities of utilizing external knowledge or tools for problem solving. By simulating human problem-solving strategies such as analogy and collaboration, we propose a multi-agent system based on LLMs named GraphTeam, for graph analysis. GraphTeam consists of five LLM-based agents from three modules, and the agents with different specialities can collaborate with each other to address complex problems. Specifically, (1) input-output normalization module: the question agent extracts and refines four key arguments from the original question, facilitating the problem understanding, and the answer agent organizes the results to meet the output requirement; (2) external knowledge retrieval module: we first build a knowledge base consisting of relevant documentation and experience information, and then the search agent retrieves the most relevant entries for each question. (3) problem-solving module: given the retrieved information from search agent, the coding agent uses established algorithms via programming to generate solutions, and in case the coding agent does not work, the reasoning agent will directly compute the results without programming. Extensive experiments on six graph analysis benchmarks demonstrate that GraphTeam achieves state-of-the-art performance with an average 25.85% improvement over the best baseline in terms of accuracy. The code and data are available at https://github.com/BUPT-GAMMA/GraphTeam.

While Retrieval-Augmented Generation (RAG) enhances the accuracy and relevance of responses by generative language models, it falls short in graph-based contexts where both textual and topological information are important. Naive RAG approaches inherently neglect the structural intricacies of textual graphs, resulting in a critical gap in the generation process. To address this challenge, we introduce Graph Retrieval-Augmented Generation (GRAG), which significantly enhances both the retrieval and generation processes by emphasizing the importance of subgraph structures. Unlike RAG approaches that focus solely on text-based entity retrieval, GRAG maintains an acute awareness of graph topology, which is crucial for generating contextually and factually coherent responses. Our GRAG approach consists of four main stages: indexing of k-hop ego-graphs, graph retrieval, soft pruning to mitigate the impact of irrelevant entities, and generation with pruned textual subgraphs. GRAG's core workflow-retrieving textual subgraphs followed by soft pruning-efficiently identifies relevant subgraph structures while avoiding the computational infeasibility typical of exhaustive subgraph searches, which are NP-hard. Moreover, we propose a novel prompting strategy that achieves lossless conversion from textual subgraphs to hierarchical text descriptions. Extensive experiments on graph multi-hop reasoning benchmarks demonstrate that in scenarios requiring multi-hop reasoning on textual graphs, our GRAG approach significantly outperforms current state-of-the-art RAG methods while effectively mitigating hallucinations.

Many graph representation learning (GRL) problems are dynamic, with millions of edges added or removed per second. A fundamental workload in this setting is dynamic link prediction: using a history of graph updates to predict whether a given pair of vertices will become connected. Recent schemes for link prediction in such dynamic settings employ Transformers, modeling individual graph updates as single tokens. In this work, we propose HOT: a model that enhances this line of works by harnessing higher-order (HO) graph structures; specifically, k-hop neighbors and more general subgraphs containing a given pair of vertices. Harnessing such HO structures by encoding them into the attention matrix of the underlying Transformer results in higher accuracy of link prediction outcomes, but at the expense of increased memory pressure. To alleviate this, we resort to a recent class of schemes that impose hierarchy on the attention matrix, significantly reducing memory footprint. The final design offers a sweetspot between high accuracy and low memory utilization. HOT outperforms other dynamic GRL schemes, for example achieving 9%, 7%, and 15% higher accuracy than - respectively - DyGFormer, TGN, and GraphMixer, for the MOOC dataset. Our design can be seamlessly extended towards other dynamic GRL workloads.

Graph learning has become indispensable for interpreting and harnessing relational data in diverse fields, ranging from recommendation systems to social network analysis. In this context, a variety of GNNs have emerged as promising methodologies for encoding the structural information of graphs. By effectively capturing the graph's underlying structure, these GNNs have shown great potential in enhancing performance in graph learning tasks, such as link prediction and node classification. However, despite their successes, a significant challenge persists: these advanced methods often face difficulties in generalizing to unseen graph data that significantly differs from the training instances. In this work, our aim is to advance the graph learning paradigm by developing a general graph foundation model. This model is designed to understand the complex topological patterns present in diverse graph data, enabling it to excel in zero-shot graph learning tasks across different downstream datasets. To achieve this goal, we address several key technical challenges in our OpenGraph model. Firstly, we propose a unified graph tokenizer to adapt our graph model to generalize well on unseen graph data, even when the underlying graph properties differ significantly from those encountered during training. Secondly, we develop a scalable graph transformer as the foundational encoder, which effectively captures node-wise dependencies within the global topological context. Thirdly, we introduce a data augmentation mechanism enhanced by a LLM to alleviate the limitations of data scarcity in real-world scenarios. Extensive experiments validate the effectiveness of our framework. By adapting our OpenGraph to new graph characteristics and comprehending the nuances of diverse graphs, our approach achieves remarkable zero-shot graph learning performance across various settings and domains.

This work introduces DiGress, a discrete denoising diffusion model for generating graphs with categorical node and edge attributes. Our model utilizes a discrete diffusion process that progressively edits graphs with noise, through the process of adding or removing edges and changing the categories. A graph transformer network is trained to revert this process, simplifying the problem of distribution learning over graphs into a sequence of node and edge classification tasks. We further improve sample quality by introducing a Markovian noise model that preserves the marginal distribution of node and edge types during diffusion, and by incorporating auxiliary graph-theoretic features. A procedure for conditioning the generation on graph-level features is also proposed. DiGress achieves state-of-the-art performance on molecular and non-molecular datasets, with up to 3x validity improvement on a planar graph dataset. It is also the first model to scale to the large GuacaMol dataset containing 1.3M drug-like molecules without the use of molecule-specific representations.

Graph embedding methods produce unsupervised node features from graphs that can then be used for a variety of machine learning tasks. Modern graphs, particularly in industrial applications, contain billions of nodes and trillions of edges, which exceeds the capability of existing embedding systems. We present PyTorch-BigGraph (PBG), an embedding system that incorporates several modifications to traditional multi-relation embedding systems that allow it to scale to graphs with billions of nodes and trillions of edges. PBG uses graph partitioning to train arbitrarily large embeddings on either a single machine or in a distributed environment. We demonstrate comparable performance with existing embedding systems on common benchmarks, while allowing for scaling to arbitrarily large graphs and parallelization on multiple machines. We train and evaluate embeddings on several large social network graphs as well as the full Freebase dataset, which contains over 100 million nodes and 2 billion edges.