Complementary Strengths: Combining Geometric and Topological Approaches for Community Detection

TL;DR

This paper introduces a hybrid community detection framework combining geometric spectral embedding and topological data analysis, improving robustness across diverse network structures.

Contribution

It presents a novel unified approach that integrates spectral embedding with TDA for community detection, leveraging their complementary strengths.

Findings

Performs comparably to Louvain on modular networks

Demonstrates robustness across synthetic benchmarks

Highlights the benefit of hybrid geometric-topological methods

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.