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Learning Persistent Community Structures in Dynamic Networks via Topological Data Analysis

Dexu Kong, Anping Zhang, Yang Li

TL;DR

This paper tackles the challenge of dynamic community detection with temporal consistency by integrating Topological Data Analysis (TDA) into an end-to-end deep clustering framework. It introduces Matrix Factorization Clustering (MFC) to preserve node embedding structure during clustering and Topological Regularization (TopoReg) to enforce persistent inter-community topology across neighboring snapshots using persistence diagrams. The approach jointly optimizes clustering quality and topological stability, leveraging a differentiable community-network representation and Wasserstein-distance based regularization through Weight Rank Clique Filtration. Experiments on synthetic and real-world dynamic networks show that MFC+TopoReg improves clustering accuracy and preserves topology more robustly than baselines, including in settings with unknown or changing numbers of communities. This work provides a principled, topology-aware method for dynamic graph clustering with practical implications for reliable analysis of evolving networks.

Abstract

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

Learning Persistent Community Structures in Dynamic Networks via Topological Data Analysis

TL;DR

This paper tackles the challenge of dynamic community detection with temporal consistency by integrating Topological Data Analysis (TDA) into an end-to-end deep clustering framework. It introduces Matrix Factorization Clustering (MFC) to preserve node embedding structure during clustering and Topological Regularization (TopoReg) to enforce persistent inter-community topology across neighboring snapshots using persistence diagrams. The approach jointly optimizes clustering quality and topological stability, leveraging a differentiable community-network representation and Wasserstein-distance based regularization through Weight Rank Clique Filtration. Experiments on synthetic and real-world dynamic networks show that MFC+TopoReg improves clustering accuracy and preserves topology more robustly than baselines, including in settings with unknown or changing numbers of communities. This work provides a principled, topology-aware method for dynamic graph clustering with practical implications for reliable analysis of evolving networks.

Abstract

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
Paper Structure (13 sections, 7 equations, 8 figures, 2 tables, 2 algorithms)

This paper contains 13 sections, 7 equations, 8 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Deep Graph Clustering
  4. Topological Graph Analysis
  5. Notations and Problem Formulation
  6. Methodology
  7. Matrix Factorization Clustering
  8. Topological Regularization of Dynamic Clustering Consistency
  9. Experiments and Results
  10. Experiments on Synthetic Data
  11. Experiments on Real-world Datasets
  12. Conclusion
  13. Acknowledgments

Figures (8)

  • Figure 1: Inconsistent inter-community structure in dynamic community detection. The top row shows three snapshots of a dynamic graph constructed at the vertex level, undergoing a transient perturbation; Different node colors represent their true community labels. The inconsistent communities are outlined by rectangles. The second row shows the corresponding community-level networks, which exhibit a falsely detected merge.
  • Figure 2: Framework of matrix factorization clustering. It consists of a graph auto-encoder and a clustering module.
  • Figure 3: Illustration of topological regularization. A sequential process across three time steps is shown. Rows trace graph evolution with columns showing snapshots, embeddings, community graphs, and persistence barcodes. Different colors are used to differentiate the real category labels. Red arrows highlight the temporal consistency loss on persistence barcodes and the backpropagation path for the $t$th snapshot $G_t$.
  • Figure 4: A demo showing how the community graph is computed. The first row shows the clustering results, and the second row shows the community graphs derived from them. From left to right, the assignment distribution of the nodes marked in red changes as the gradient of the edge weight of the community graph decreases, and the corresponding topology changes.
  • Figure 5: Illustration of Weight Rank Clique Filtration (WRCF) applied to a toy graph. The first row shows a weighted graph, followed by the simple complex under three levels of filtration, and the second row shows the persistence barcode corresponding to the above filtration. The black lines represent the 0th persistent Betti number, while the red line represents the 1st persistent Betti number.
  • ...and 3 more figures