Iterative Ricci-Foster Curvature Flow with GMM-Based Edge Pruning: A Novel Approach to Community Detection

2025-11-12

AI Summary

To address the inefficiency and limited interpretability of community detection in complex networks, this paper proposes an iterative method based on Ricci–Foster curvature flow over graphs. It dynamically reweights edges using effective resistance distances computed via the pseudoinverse of the graph Laplacian and employs a Gaussian Mixture Model (GMM) to model edge curvature distributions for adaptive edge pruning. This work is the first to integrate Foster-type Ricci curvature with GMM-driven pruning, substantially improving computational efficiency while avoiding the high complexity of conventional Ollivier–Ricci flow. Experiments on Stochastic Block Model (SBM) synthetic networks demonstrate that the method achieves significantly higher Adjusted Rand Index than the baseline combining Ollivier–Ricci flow with spectral clustering, robustly recovering ground-truth community structures. The approach establishes a principled, efficient, and scalable paradigm for community detection.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Social Networks and Social Media: Computational social science

Abstract

Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the nodes. The latter computation is known to be done by pseudo-inverting the graph Laplacian matrix. At that, our approach is alternative to one based on Ollivier-Ricci geometric flow for community detection on graphs, significantly outperforming it in terms of computation time. In our proposed method, iterations of Foster-Ricci flow that highlight network regions of different curvature -- are followed by a Gaussian Mixture Model (GMM) separation heuristic. That allows to classify edges into''strong''(intra-community) and''weak''(inter-community) groups, followed by a systematic pruning of the former to isolate communities. We benchmark our algorithm on synthetic networks generated from the Stochastic Block Model (SBM), evaluating performance with the Adjusted Rand Index (ARI). Our results demonstrate that proposed framework robustly recovers the planted community structure of SBM-s, establishing Ricci-Foster Flow with GMM-clustering as a principled and computationally effective new tool for network analysis, tested against alternative Ricci-Ollivier flow coupled with spectral clustering.

Problem

• Develops a novel community detection method using iterative Ricci-Foster curvature flow
• Proposes GMM-based edge pruning to separate intra-community and inter-community connections
• Benchmarks performance against alternative methods using synthetic networks and ARI

Innovation

• Iterative Ricci-Foster curvature flow updates edge weights
• GMM-based edge pruning separates strong and weak edges
• Computationally faster than Ollivier-Ricci flow with spectral clustering