Weighted Growing Simplicial Complexes

Abstract

Simplicial complexes describe collaboration networks, protein interaction networks and brain networks and in general network structures in which the interactions can include more than two nodes. In real applications, often simplicial complexes are weighted. Here we propose a non-equilibrium model for weighted growing simplicial complexes. The proposed dynamics is able to generate weighted simplicial complexes with a rich interplay between weights and topology emerging not just at the level of nodes and links, but also at the level of faces of higher dimension.

(14 pages, 6 figures)

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• Weighted simplicial complexes and their representation power of higher-order network data and topology
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• Growing scale-free simplices
• Network Geometry and Complexity
• Dense Power-law Networks and Simplicial Complexes
• A class of models for random hypergraphs
• Persistent homology of unweighted complex networks via discrete Morse theory
• Spectral properties of hyperbolic nano-networks with tunable aggregation of simplexes
• Geometry, Topology and Simplicial Synchronization
• On the reorderability of node-filtered order complexes
• Random Simplicial Complexes: Models and Phenomena
• Quantum statistics in Network Geometry with Fractional Flavor
• Forman-Ricci curvature and Persistent homology of unweighted complex networks
• Synchronizability in randomized weighted simplicial complexes
• Constraints and Entropy in a Model of Network Evolution
• Growing Hypergraphs with Preferential Linking
• A Generative Hypergraph Model for Double Heterogeneity
• Combinatorial Properties for a Class of Simplicial Complexes Extended from Pseudo-fractal Scale-free Web
• Edge corona product as an approach to modeling complex simplical networks
• On algebraic and combinatorial properties of weighted simplicial complexes