This lack of rich textual edge annotations significantly limits the exploration of contextual relationships between entities, hindering deeper insights into graph-structured data.

Specifically, we show that contrary to sets, elements in a graph are not entirely unordered and there is a unique partial order for nodes and edges. With this partial order,PARD generates a graph in a block-by-block, autoregressivefashion, where each block'sprobability isconditionally modeled by a shared diffusion model with an equivariant network.

Dynamic text-attributed graphs (DyTAGs) are prevalent in various real-world scenarios, where each node and edge are associated with text descriptions, and both the graph structure and text descriptions evolve over time. Despite their broad applicability, there is a notable scarcity of benchmark datasets tailored to DyTAGs, which hinders the potential advancement in many research fields. To address this gap, we introduce Dynamic Text-attributed Graph Benchmark (DTGB), a collection of large-scale, time-evolving graphs from diverse domains, with nodes and edges enriched by dynamically changing text attributes and categories. To facilitate the use of DTGB, we design standardized evaluation procedures based on four real-world use cases: future link prediction, destination node retrieval, edge classification, and textual relation generation. These tasks require models to understand both dynamic graph structures and natural language, highlighting the unique challenges posed by DyTAGs.

Reasoning on large-scale knowledge graphs has been long dominated by embedding methods. While path-based methods possess the inductive capacity that embeddings lack, their scalability is limited by the exponential number of paths. Here we present A*Net, a scalable path-based method for knowledge graph reasoning. Inspired by the A* algorithm for shortest path problems, our A*Net learns a priority function to select important nodes and edges at each iteration, to reduce time and memory footprint for both training and inference. The ratio of selected nodes and edges can be specified to trade off between performance and efficiency. Experiments on both transductive and inductive knowledge graph reasoning benchmarks show that A*Net achieves competitive performance with existing state-of-the-art path-based methods, while merely visiting 10% nodes and 10% edges at each iteration. On a million-scale dataset ogbl-wikikg2, A*Net not only achieves a new state-of-the-art result, but also converges faster than embedding methods. A*Net is the first path-based method for knowledge graph reasoning at such scale.

Graph Edit Distance (GED) measures the (dis-)similarity between two given graphs in terms of the minimum-cost edit sequence, which transforms one graph to the other.GED is related to other notions of graph similarity, such as graph and subgraph isomorphism, maximum common subgraph, etc. However, the computation of exact GED is NP-Hard, which has recently motivated the design of neural models for GED estimation.However, they do not explicitly account for edit operations with different costs. In response, we propose $\texttt{GraphEdX}$, a neural GED estimator that can work with general costs specified for the four edit operations, viz., edge deletion, edge addition, node deletion, and node addition.We first present GED as a quadratic assignment problem (QAP) that incorporates these four costs.Then, we represent each graph as a set of node and edge embeddings and use them to design a family of neural set divergence surrogates. We replace the QAP terms corresponding to each operation with their surrogates. Computing such neural set divergence requires aligning nodes and edges of the two graphs.We learn these alignments using a Gumbel-Sinkhorn permutation generator, additionally ensuring that the node and edge alignments are consistent with each other. Moreover, these alignments are cognizant of both the presence and absence of edges between node pairs.Through extensive experiments on several datasets, along with a variety of edit cost settings, we show that $\texttt{GraphEdX}$ consistently outperforms state-of-the-art methods and heuristics in terms of prediction error.

Successful graph generation depends on the accurate estimation of the joint distribution of graph components such as nodes and edges from training data. While recent deep neural networks have demonstrated sampling of realistic graphs together with diffusion models, however, they still suffer from oversmoothing problems which are inherited from conventional graph convolution and thus high-frequency characteristics of nodes and edges become intractable. To overcome such issues and generate graphs with high fidelity, this paper introduces a novel approach that captures the dependency between nodes and edges at multiple resolutions in the spectral space. By modeling the joint distribution of node and edge signals in a shared graph wavelet space, together with a score-based diffusion model, we propose a Wavelet Graph Diffusion Model (Wave-GD) which lets us sample synthetic graphs with real-like frequency characteristics of nodes and edges. Experimental results on four representative benchmark datasets validate the superiority of the Wave-GD over existing approaches, highlighting its potential for a wide range of applications that involve graph data.

Large Language Models (LLMs) increasingly rely on knowledge graphs for factual reasoning, yet how retrieval design shapes their performance remains unclear. We examine how question decomposition changes the retrieved subgraph's content and structure. Using a hybrid retrieval function that controls the importance of initial question and sub-questions, we show that subquestion-based retrieval improves content precision, but yields disjoint subgraphs, while question-based retrieval maintains structure at the cost of relevance. Optimal performance arises between these extremes, revealing that balancing retrieval content and structure is key to effective LLM reasoning over structured knowledge.