Topology-Based Detection and Modularity Analysis of Communities in Email Communication Networks

This study investigates the structural organization of an email communication network constructed from the SNAP Enron dataset, where nodes represent individual email addresses and edges correspond to communication links between them. Communities within the network were identified using the Label Propagation Algorithm (LPA), yielding 35 distinct groups. To evaluate the structural coherence and significance of these communities, we integrated two complementary analytical frameworks: Persistent Homology, from Topological Data Analysis (TDA), and Modularity, a key metric in network theory. Persistent homology was utilized to detect enduring topological features—such as connected components, loops, and voids—that characterize the intrinsic structure of each community across varying filtration scales. Modularity analysis, in turn, quantified the relative density of intra- and inter-community connections. Combining these approaches enabled the classification of communities as non-significant, significant, influential, or highly influential. The findings reveal a strong correlation between persistent topological features and high modularity scores, offering deeper insights into the stability, cohesion, and influence of communities in large-scale social communication networks.