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Cliques Are Bricks for k-CT Graphs

Author

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  • Václav Snášel

    (Department of Computer Science, Faculty of Electrical Engineering and Computer Science, VŠB-Technical University of Ostrava, 17. listopadu 15/2172, 708 33 Ostrava, Czech Republic)

  • Pavla Dráždilová

    (Department of Computer Science, Faculty of Electrical Engineering and Computer Science, VŠB-Technical University of Ostrava, 17. listopadu 15/2172, 708 33 Ostrava, Czech Republic)

  • Jan Platoš

    (Department of Computer Science, Faculty of Electrical Engineering and Computer Science, VŠB-Technical University of Ostrava, 17. listopadu 15/2172, 708 33 Ostrava, Czech Republic)

Abstract

Many real networks in biology, chemistry, industry, ecological systems, or social networks have an inherent structure of simplicial complexes reflecting many-body interactions. Over the past few decades, a variety of complex systems have been successfully described as networks whose links connect interacting pairs of nodes. Simplicial complexes capture the many-body interactions between two or more nodes and generalized network structures to allow us to go beyond the framework of pairwise interactions. Therefore, to analyze the topological and dynamic properties of simplicial complex networks, the closed trail metric is proposed here. In this article, we focus on the evolution of simplicial complex networks from clicks and k-CT graphs. This approach is used to describe the evolution of real simplicial complex networks. We conclude with a summary of composition k-CT graphs (glued graphs); their closed trail distances are in a specified range.

Suggested Citation

  • Václav Snášel & Pavla Dráždilová & Jan Platoš, 2021. "Cliques Are Bricks for k-CT Graphs," Mathematics, MDPI, vol. 9(11), pages 1-9, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1160-:d:559191
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    References listed on IDEAS

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    1. Hernández Serrano, Daniel & Sánchez Gómez, Darío, 2020. "Centrality measures in simplicial complexes: Applications of topological data analysis to network science," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    2. Iacopo Iacopini & Giovanni Petri & Alain Barrat & Vito Latora, 2019. "Simplicial models of social contagion," Nature Communications, Nature, vol. 10(1), pages 1-9, December.
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