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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.11496 |
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Table of Contents:
- 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.