Weighted simplicial complexes and their representation power of higher-order network data and topology
| Autor: | Federica Baccini, Filippo Geraci, Ginestra Bianconi |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
Computational Geometry (cs.CG)
Social and Information Networks (cs.SI) FOS: Computer and information sciences Physics - Physics and Society J.2 FOS: Physical sciences Computer Science - Social and Information Networks Physics and Society (physics.soc-ph) Disordered Systems and Neural Networks (cond-mat.dis-nn) Condensed Matter - Disordered Systems and Neural Networks FOS: Mathematics Computer Science - Computational Geometry Algebraic Topology (math.AT) Mathematics - Algebraic Topology |
| Zdroj: | Physical review. E. 106(3-1) |
| ISSN: | 2470-0053 |
| Popis: | Hypergraphs and simplical complexes both capture the higher-order interactions of complex systems, ranging from higher-order collaboration networks to brain networks. One open problem in the field is what should drive the choice of the adopted mathematical framework to describe higher-order networks starting from data of higher-order interactions. Unweighted simplicial complexes typically involve a loss of information of the data, though having the benefit to capture the higher-order topology of the data. In this work we show that weighted simplicial complexes allow to circumvent all the limitations of unweighted simplicial complexes to represent higher-order interactions. In particular, weighted simplicial complexes can represent higher-order networks without loss of information, allowing at the same time to capture the weighted topology of the data. The higher-order topology is probed by studying the spectral properties of suitably defined weighted Hodge Laplacians displaying a normalized spectrum. The higher-order spectrum of (weighted) normalized Hodge Laplacians is here studied combining cohomology theory with information theory. In the proposed framework, we quantify and compare the information content of higher-order spectra of different dimension using higher-order spectral entropies and spectral relative entropies. The proposed methodology is tested on real higher-order collaboration networks and on the weighted version of the simplicial complex model "Network Geometry with Flavor". Comment: 20 pages, 11 figures |
| Databáze: | OpenAIRE |
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