Persistent homology method to detect block structures in weighted networks

TL;DR

This paper introduces a topological approach using persistent homology to detect block structures in weighted networks, providing a new perspective that complements existing stochastic block models.

Contribution

A novel topological method based on persistence diagrams for identifying block structures in weighted networks, demonstrating robustness and consistency with stochastic block models.

Findings

Persistence diagrams reveal distinct features for different block structures.

Method remains effective despite stochastic variations and hyperparameter changes.

Results align with weighted stochastic block model when tested on unknown latent structures.

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.