How Local Separators Shape Community Structure in Large Networks
Sarah Frenkel, Johannes Carmesin
TL;DR
This paper investigates local separator methods as scalable, bottleneck-driven alternatives to modularity-based community detection in large networks. It defines and compares 1-separator and 2-separator decompositions against standard algorithms (Infomap, Label Propagation, Leiden Modularity, Best Multilevel) across networks including Netscience and road networks, highlighting the strengths and limitations of modularity-based evaluation. The results show that the local 1-separator reliably identifies the densest communities, while the local 2-separator reveals hierarchical structure though it can over-fragment small clusters; road networks in particular benefit from these methods. Overall, local separators offer a practical, interpretable decomposition mechanism that complements traditional approaches and is well suited for transportation and infrastructure analysis.
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.