Effective and Efficient Conductance-based Community Search at Billion Scale

2025-08-02

AI Summary

This paper addresses the overlooked issue of external sparsity in community search by formally introducing the Conductance-based Community Search (CCS) problem: given a query vertex, find the connected subgraph containing it that minimizes conductance—the ratio of cut edges to internal volume. CCS is proven NP-hard. To solve it efficiently, the authors propose SCCS, a four-stage algorithm: (1) local graph sampling to reduce scale; (2) seed selection; (3) gain-driven expansion; and (4) verification-based pruning—jointly optimizing internal cohesiveness and external sparsity. Extensive experiments on billion-scale real-world and synthetic graphs demonstrate that SCCS significantly outperforms state-of-the-art methods in effectiveness, efficiency, and scalability.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• 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
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Community search is a widely studied semi-supervised graph clustering problem, retrieving a high-quality connected subgraph containing the user-specified query vertex. However, existing methods primarily focus on cohesiveness within the community but ignore the sparsity outside the community, obtaining sub-par results. Inspired by this, we adopt the well-known conductance metric to measure the quality of a community and introduce a novel problem of conductance-based community search (CCS). CCS aims at finding a subgraph with the smallest conductance among all connected subgraphs that contain the query vertex. We prove that the CCS problem is NP-hard. To efficiently query CCS, a four-stage subgraph-conductance-based community search algorithm, SCCS, is proposed. Specifically, we first greatly reduce the entire graph using local sampling techniques. Then, a three-stage local optimization strategy is employed to continuously refine the community quality. Namely, we first utilize a seeding strategy to obtain an initial community to enhance its internal cohesiveness. Then, we iteratively add qualified vertices in the expansion stage to guarantee the internal cohesiveness and external sparsity of the community. Finally, we gradually remove unqualified vertices during the verification stage. Extensive experiments on real-world datasets containing one billion-scale graph and synthetic datasets show the effectiveness, efficiency, and scalability of our solutions.

Problem

• Finding high-quality connected subgraphs using conductance metric
• Addressing NP-hard conductance-based community search problem
• Efficiently reducing graph size and refining community quality

Innovation

• Uses conductance metric for community quality
• Local sampling reduces graph size efficiently
• Three-stage local optimization refines community