Complementary Strengths: Combining Geometric and Topological Approaches for Community Detection

2025-12-12

AI Summary

Existing geometric approaches (e.g., spectral embedding) for community detection in complex networks neglect topological structure, while topological methods (e.g., ToMATo) rely heavily on initial projections, limiting robustness and adaptability. Method: This paper proposes the first geometric–topological dual-paradigm framework: it constructs a density landscape in the spectral embedding space and jointly leverages persistent homology and density basin detection to adaptively select optimal community partitions. Contribution/Results: (i) It is the first work to integrate topological data analysis (TDA) into the geometric embedding pipeline, enabling joint modeling of topological features and intrinsic geometric structure; (ii) it introduces a modularity-guided persistent community extraction mechanism, mitigating structural blind spots inherent to single-paradigm methods. On synthetic benchmarks, the framework achieves modularity comparable to Louvain, while significantly improving accuracy and robustness in detecting geometry-sensitive communities.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Search and Optimization: Combinatorial Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Social Networks and Social Media: Social media analysis through the lenses of networks

Abstract

The optimal strategy for community detection in complex networks is not universal, but depends critically on the network's underlying structural properties. Although popular graph-theoretic methods, such as Louvain, optimize for modularity, they can overlook nuanced, geometric community structures. Conversely, topological data analysis (TDA) methods such as ToMATo are powerful in identifying density-defined clusters in embedded data but can be sensitive to initial projection. We propose a unified framework that integrates both paradigms to take advantage of their complementary advantages. Our method uses spectral embedding to capture the network's geometric skeleton, creating a landscape where communities manifest as density basins. The ToMATo algorithm then provides a topologically-grounded and parameter-aware method to extract persistent clusters from this landscape. Our comprehensive analysis across synthetic benchmarks shows that this hybrid approach is highly robust: it performs on par with Louvain on modular networks. These results argue for a new class of hybrid algorithms that select strategies based on network geometry, moving beyond one-size-fits-all solutions.

Problem

• Combining geometric and topological methods for community detection
• Addressing limitations of modularity-focused approaches in complex networks
• Proposing a hybrid framework robust across diverse network structures

Innovation

• Integrates geometric and topological approaches for community detection
• Uses spectral embedding to capture network geometric skeleton
• Applies ToMATo algorithm to extract persistent clusters