Efficient Community Detection in Large-Scale Dynamic Networks Using Topological Data Analysis

TL;DR

This paper introduces a novel topological data analysis approach for detecting and tracking community structures in large-scale dynamic networks, leveraging persistence-based methods and efficient algorithms.

Contribution

It extends topological data analysis to general networks through community trees and develops algorithms for dynamic updating, enabling effective community detection in evolving networks.

Findings

Successfully detects clique communities in dynamic social networks

Tracks structural changes over time with stability thresholds

Demonstrates effectiveness on large-scale, time-varying networks

Abstract

In this paper, we propose a method that extends the persistence-based topological data analysis (TDA) that is typically used for characterizing shapes to general networks. We introduce the concept of the community tree, a tree structure established based on clique communities from the clique percolation method, to summarize the topological structures in a network from a persistence perspective. Furthermore, we develop efficient algorithms to construct and update community trees by maintaining a series of clique graphs in the form of spanning forests, in which each spanning tree is built on an underlying Euler Tour tree. With the information revealed by community trees and the corresponding persistence diagrams, our proposed approach is able to detect clique communities and keep track of the major structural changes during their evolution given a stability threshold. The results demonstrate its effectiveness in extracting useful structural insights for time-varying social networks.