Persistent homology method to detect block structures in weighted networks

Abstract

Unravelling the block structure of a network is critical for studying macroscopic features and community-level dynamics. The weighted stochastic block model (WSBM), a variation of the traditional stochastic block model, is designed for weighted networks, but it is not always optimal. We introduce a novel topological method to study the block structure of weighted networks by comparing their persistence diagrams. We found persistence diagrams of networks with different block structures show distinct features, sufficient to distinguish. Moreover, the overall characteristics are preserved even with more stochastic examples or modified hyperparameters. Finally, when random graphs whose latent block structure is unknown are tested, results from persistence diagram analysis are consistent with their weighted stochastic block model. Although this topological method cannot completely replace the original WSBM method for some reasons, it is worth to be investigated further.

arXiv comment7 pages, 7 figures; Submitted for University of Oxford Mathematics Part C Networks course

References in corpus (6)

• The architecture of complex weighted networks
• Stochastic blockmodels and community structure in networks
• Statistical topological data analysis using persistence landscapes
• A Bayesian Approach to Network Modularity
• Adapting the Stochastic Block Model to Edge-Weighted Networks
• Valued Ties Tell Fewer Lies: Why Not To Dichotomize Network Edges With Thresholds