Beyond Homophily: Community Search on Heterophilic Graphs

2026-01-05

arXiv.org

AI Summary

This work addresses the limitations of traditional community search methods, which rely on homophily assumptions and struggle to identify semantically coherent communities in heterophilous graphs. To overcome this challenge, the authors propose AdaptCS, a novel framework that unifies the handling of both homophilous and heterophilous relationships. AdaptCS leverages a multi-frequency graph signal decoupling encoder, memory-efficient low-rank optimization, and an adaptive community scoring (ACS) mechanism to enable efficient and accurate community search in graphs with unknown edge semantics and heterophily. Experimental results demonstrate that AdaptCS achieves an average F1-score improvement of 11% across multiple benchmarks, exhibits strong robustness to varying degrees of heterophily, and delivers up to two orders of magnitude faster runtime compared to existing approaches.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Search

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Social Networks and Social Media: Social mining and social search on the Web
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Community search aims to identify a refined set of nodes that are most relevant to a given query, supporting tasks ranging from fraud detection to recommendation. Unlike homophilic graphs, many real-world networks are heterophilic, where edges predominantly connect dissimilar nodes. Therefore, structural signals that once reflected smooth, low-frequency similarity now appear as sharp, high-frequency contrasts. However, both classical algorithms (e.g., k-core, k-truss) and recent ML-based models struggle to achieve effective community search on heterophilic graphs, where edge signs or semantics are generally unknown. Algorithm-based methods often return communities with mixed class labels, while GNNs, built on homophily, smooth away meaningful signals and blur community boundaries. Therefore, we propose Adaptive Community Search (AdaptCS), a unified framework featuring three key designs: (i) an AdaptCS Encoder that disentangles multi-hop and multi-frequency signals, enabling the model to capture both smooth (homophilic) and contrastive (heterophilic) relations; (ii) a memory-efficient low-rank optimization that removes the main computational bottleneck and ensures model scalability; and (iii) an Adaptive Community Score (ACS) that guides online search by balancing embedding similarity and topological relations. Extensive experiments on both heterophilic and homophilic benchmarks demonstrate that AdaptCS outperforms the best-performing baseline by an average of 11% in F1-score, retains robustness across heterophily levels, and achieves up to 2 orders of magnitude speedup.

Problem

• community search
• heterophilic graphs
• graph neural networks
• homophily
• structural signals

Innovation

• heterophilic graphs
• community search
• multi-frequency signals
• low-rank optimization
• adaptive community scoring