  Dynamic community detection methods often lack effective mechanisms to ensure
temporal consistency, hindering the analysis of network evolution. In this
paper, we propose a novel deep graph clustering framework with temporal
consistency regularization on inter-community structures, inspired by the
concept of minimal network topological changes within short intervals.
Specifically, to address the representation collapse problem, we first
introduce MFC, a matrix factorization-based deep graph clustering algorithm
that preserves node embedding. Based on static clustering results, we construct
probabilistic community networks and compute their persistence homology, a
robust topological measure, to assess structural similarity between them.
Moreover, a novel neural network regularization TopoReg is introduced to ensure
the preservation of topological similarity between inter-community structures
over time intervals. Our approach enhances temporal consistency and clustering
accuracy on real-world datasets with both fixed and varying numbers of
communities. It is also a pioneer application of TDA in temporally persistent
community detection, offering an insightful contribution to field of network
analysis. Code and data are available at the public git repository:
https://github.com/kundtx/MFC_TopoReg
