Weighted simplicial complexes and their representation power of higher-order network data and topology

被引:47
作者
Baccini, Federica [1 ,2 ]
Geraci, Filippo [2 ]
Bianconi, Ginestra [3 ,4 ]
机构
[1] Univ Pisa, Dept Comp Sci, I-56127 Pisa, Italy
[2] CNR, Inst Informat & Telemat, I-56124 Pisa, Italy
[3] Queen Mary Univ London, Sch Math Sci, London E1 4NS, England
[4] British Lib, Alan Turing Inst, London NW1 2DB, England
关键词
LAPLACE OPERATORS; RANDOM-WALKS;
D O I
10.1103/PhysRevE.106.034319
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
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 one 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 one 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 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."
引用
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页数:17
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