Graph), a comprehensive benchmark of graph-based problem solving designed in natural language.

A more detailed picture of the graph can be obtained by looking at its degree distribution, which is presented in Figure 4.

The ability to gather new knowledge about the world is a fundamental aspect of intelligence.

The metric backbone of a weighted graph is the union of all-pairs shortest paths. It is obtained by removing all edges $(u,v)$ that are not the shortest path between $u$ and $v$. In networks with well-separated communities, the metric backbone tends to preserve many inter-community edges, because these edges serve as bridges connecting two communities, but tends to delete many intra-community edges because the communities are dense. This suggests that the metric backbone would dilute or destroy the community structure of the network. However, this is not borne out by prior empirical work, which instead showed that the metric backbone of real networks preserves the community structure of the original network well. In this work, we analyze the metric backbone of a broad class of weighted random graphs with communities, and we formally prove the robustness of the community structure with respect to the deletion of all the edges that are not in the metric backbone. An empirical comparison of several graph sparsification techniques confirms our theoretical finding and shows that the metric backbone is an efficient sparsifier in the presence of communities.

Graph Neural Networks (GNNs) have recently been applied to graph learning tasks and achieved state-of-the-art (SOTA) results. However, many competitive methods run GNNs multiple times with subgraph extraction and customized labeling to capture information that is hard for normal GNNs to learn. Such operations are time-consuming and do not scale to large graphs. In this paper, we propose an efficient GNN framework called Geodesic GNN (GDGNN) that requires only one GNN run and injects conditional relationships between nodes into the model without labeling. This strategy effectively reduces the runtime of subgraph methods. Specifically, we view the shortest paths between two nodes as the spatial graph context of the neighborhood around them.

Graph-based Retrieval-Augmented Generation (GraphRAG) enhances Large Language Models (LLMs) by incorporating external knowledge from linearized subgraphs retrieved from knowledge graphs. However, LLMs struggle to interpret the relational and topological information in these inputs, resulting in hallucinations that are inconsistent with the retrieved knowledge. To analyze how LLMs attend to and retain structured knowledge during generation, we propose two lightweight interpretability metrics: Path Reliance Degree (PRD), which measures over-reliance on shortest-path triples, and Semantic Alignment Score (SAS), which assesses how well the model's internal representations align with the retrieved knowledge. Through empirical analysis on a knowledge-based QA task, we identify failure patterns associated with over-reliance on salient paths and weak semantic grounding, as indicated by high PRD and low SAS scores. We further develop a lightweight post-hoc hallucination detector, Graph Grounding and Alignment (GGA), which outperforms strong semantic and confidence-based baselines across AUC and F1. By grounding hallucination analysis in mechanistic interpretability, our work offers insights into how structural limitations in LLMs contribute to hallucinations, informing the design of more reliable GraphRAG systems in the future.