# Learning Persistent Community Structures in Dynamic Networks via Topological Data Analysis

arXiv: https://arxiv.org/abs/2401.03194 · HTML: https://mlsanity.com/paper/2401.03194/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 44 references that are in the map.
- First posted on arXiv 6 Jan 2024.

## Builds on (most cited first, 15 of 15)

- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [Generative Adversarial Networks: An Overview](https://mlsanity.com/paper/1710.07035/) (2017)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [Attributed Graph Clustering: A Deep Attentional Embedding Approach](https://mlsanity.com/paper/1906.06532/) (2019)
- [Structural Deep Clustering Network](https://mlsanity.com/paper/2002.01633/) (2020)
- [Deep Graph Clustering via Dual Correlation Reduction](https://mlsanity.com/paper/2112.14772/) (2021)
- [A Topology Layer for Machine Learning](https://mlsanity.com/paper/1905.12200/) (2019)
- [Sliced Wasserstein Kernel for Persistence Diagrams](https://mlsanity.com/paper/1706.03358/) (2017)
- [Graph Attention Auto-Encoders](https://mlsanity.com/paper/1905.10715/) (2019)
- [Attention-driven Graph Clustering Network](https://mlsanity.com/paper/2108.05499/) (2021)
- [Link Prediction with Persistent Homology: An Interactive View](https://mlsanity.com/paper/2102.10255/) (2021)
- [Visual Detection of Structural Changes in Time-Varying Graphs Using Persistent Homology](https://mlsanity.com/paper/1707.06683/) (2017)
- [GloDyNE: Global Topology Preserving Dynamic Network Embedding](https://mlsanity.com/paper/2008.01935/) (2020)
- [Persistent Homology Lower Bounds on High Order Network Distances](https://mlsanity.com/paper/1507.03044/) (2015)

## Built on by (most cited first, 4 of 4)

- [RTD-Lite: Scalable Topological Analysis for Comparing Weighted Graphs in Learning Tasks](https://mlsanity.com/paper/2503.11910/) (2025)
- [Optimizing EEG Graph Structure for Seizure Detection: An Information Bottleneck and Self-Supervised Learning Approach](https://mlsanity.com/paper/2604.01595/) (2026)
- [Unfolded Laplacian Spectral Embedding: A Theoretically Grounded Approach to Dynamic Network Representation](https://mlsanity.com/paper/2508.12674/) (2025)
- [ComNetX: Local Hierarchical Adaptation for Dynamic Community Detection](https://mlsanity.com/paper/2608.16906/) (2026)

## Abstract (arXiv)

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