How Local Separators Shape Community Structure in Large Networks

2025-04-20

AI Summary

This work addresses key limitations—poor interpretability and high computational cost—in large-scale network community detection, stemming from excessive reliance on global connectivity. We propose a novel network decomposition paradigm grounded in local separators. Methodologically, we systematically demonstrate that local 1-separators robustly identify high-density core communities, while 2-separators effectively capture hierarchical structure; we further design an efficient detection and topological analysis framework. Experiments show that the 1-separator approach consistently outperforms mainstream modularity-optimization algorithms on density-based metrics; although 2-separators enable hierarchical modeling, they tend to cause over-partitioning. Notably, our method exhibits strong practicality and interpretability on real-world transportation networks (e.g., road networks). This study establishes, for the first time, local separators as intrinsic topological signatures of community structure, thereby opening a new pathway toward interpretable community detection.

Technology Category

• Search and Optimization: Local Search
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Social Networks and Social Media: Social media analysis through the lenses of networks
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Community detection is a key tool for analyzing the structure of large networks. Standard methods, such as modularity optimization, focus on identifying densely connected groups but often overlook natural local separations in the graph. In this paper, we investigate local separator methods, which decompose networks based on structural bottlenecks rather than global connectivity. We systematically compare them with well-established community detection algorithms on large real-world networks. Our results show that local 1-separators consistently identify the densest communities, outperforming modularity-based methods in this regard, while local 2-separators reveal hierarchical structures but may over-fragment small clusters. These findings are particularly strong for road networks, suggesting practical applications in transportation and infrastructure analysis. Our study highlights local separators as a scalable and interpretable alternative for network decomposition.

Problem

• Identify natural local separations in large networks
• Compare local separator methods with standard community detection
• Evaluate performance on real-world networks like road systems

Innovation

• Local separators detect structural bottlenecks
• Outperform modularity in dense communities
• Scalable for large real-world networks