IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v382y2020ics0096300320302976.html
   My bibliography  Save this article

Centrality measures in simplicial complexes: Applications of topological data analysis to network science

Author

Listed:
  • Hernández Serrano, Daniel
  • Sánchez Gómez, Darío

Abstract

Many real networks in social sciences, biological and biomedical sciences or computer science have an inherent structure of simplicial complexes reflecting many-body interactions. Therefore, to analyse topological and dynamical properties of simplicial complex networks centrality measures for simplices need to be proposed. Many of the classical complex networks centralities are based on the degree of a node, so in order to define degree centrality measures for simplices (which would characterise the relevance of a simplicial community in a simplicial network), a different definition of adjacency between simplices is required, since, contrarily to what happens in the vertex case (where there is only upper adjacency), simplices might also have other types of adjacency. The aim of these notes is threefold: first we will use the recently introduced notions of higher order simplicial degrees to propose new degree based centrality measures in simplicial complexes. These theoretical centrality measures, such as the simplicial degree centrality or the eigenvector centrality would allow not only to study the relevance of a simplicial community and the quality of its higher-order connections in a simplicial network, but also they might help to elucidate topological and dynamical properties of simplicial networks; sencond, we define notions of walks and distances in simplicial complexes in order to study connectivity of simplicial networks and to generalise, to the simplicial case, the well known closeness and betweenness centralities (needed for instance to study the relevance of a simplicial community in terms of its ability of transmitting information); third, we propose a new clustering coefficient for simplices in a simplicial network, different from the one knows so far and which generalises the standard graph clustering of a vertex. This measure should be essential to know the density of a simplicial network in terms of its simplicial communities.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:382:y:2020:i:c:s0096300320302976
    DOI: 10.1016/j.amc.2020.125331
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320302976
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125331?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Gert Sabidussi, 1966. "The centrality index of a graph," Psychometrika, Springer;The Psychometric Society, vol. 31(4), pages 581-603, December.
    2. Wang, Juan & Li, Chao & Xia, Chengyi, 2018. "Improved centrality indicators to characterize the nodal spreading capability in complex networks," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 388-400.
    3. Maletić, Slobodan & Rajković, Milan, 2014. "Consensus formation on a simplicial complex of opinions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 397(C), pages 111-120.
    4. Iacopo Iacopini & Giovanni Petri & Alain Barrat & Vito Latora, 2019. "Simplicial models of social contagion," Nature Communications, Nature, vol. 10(1), pages 1-9, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kovalenko, K. & Romance, M. & Vasilyeva, E. & Aleja, D. & Criado, R. & Musatov, D. & Raigorodskii, A.M. & Flores, J. & Samoylenko, I. & Alfaro-Bittner, K. & Perc, M. & Boccaletti, S., 2022. "Vector centrality in hypergraphs," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Shang, Yilun, 2022. "Sombor index and degree-related properties of simplicial networks," Applied Mathematics and Computation, Elsevier, vol. 419(C).
    3. Serrano, Daniel Hernández & Villarroel, Javier & Hernández-Serrano, Juan & Tocino, Ángel, 2023. "Stochastic simplicial contagion model," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    4. Václav Snášel & Pavla Dráždilová & Jan Platoš, 2021. "Cliques Are Bricks for k-CT Graphs," Mathematics, MDPI, vol. 9(11), pages 1-9, May.
    5. Hernández Serrano, Daniel & Hernández-Serrano, Juan & Sánchez Gómez, Darío, 2020. "Simplicial degree in complex networks. Applications of topological data analysis to network science," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zareie, Ahmad & Sheikhahmadi, Amir, 2019. "EHC: Extended H-index Centrality measure for identification of users’ spreading influence in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 141-155.
    2. Teqi Dai & Tiantian Ding & Qingfang Liu & Bingxin Liu, 2022. "Node Centrality Comparison between Bus Line and Passenger Flow Networks in Beijing," Sustainability, MDPI, vol. 14(22), pages 1-14, November.
    3. Federico Karagulian & Gaetano Valenti & Carlo Liberto & Matteo Corazza, 2022. "A Methodology to Estimate Functional Vulnerability Using Floating Car Data," Sustainability, MDPI, vol. 15(1), pages 1-15, December.
    4. Giacopelli, G. & Migliore, M. & Tegolo, D., 2020. "Graph-theoretical derivation of brain structural connectivity," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    5. Yao, Hongxing & Memon, Bilal Ahmed, 2019. "Network topology of FTSE 100 Index companies: From the perspective of Brexit," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1248-1262.
    6. De Masi, G. & Giovannetti, G. & Ricchiuti, G., 2013. "Network analysis to detect common strategies in Italian foreign direct investment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(5), pages 1202-1214.
    7. Sudhamayee, K. & Krishna, M. Gopal & Manimaran, P., 2023. "Simplicial network analysis on EEG signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    8. Hyuk-Soo Kwon & Jihong Lee & Sokbae Lee & Ryungha Oh, 2022. "Knowledge spillovers and patent citations: trends in geographic localization, 1976–2015," Economics of Innovation and New Technology, Taylor & Francis Journals, vol. 31(3), pages 123-147, April.
    9. Mengying Cui & David Levinson, 2018. "Accessibility analysis of risk severity," Transportation, Springer, vol. 45(4), pages 1029-1050, July.
    10. Tao, Qizhi & Li, Haoyu & Wu, Qun & Zhang, Ting & Zhu, Yingjun, 2019. "The dark side of board network centrality: Evidence from merger performance," Journal of Business Research, Elsevier, vol. 104(C), pages 215-232.
    11. Jiang, Lincheng & Zhao, Xiang & Ge, Bin & Xiao, Weidong & Ruan, Yirun, 2019. "An efficient algorithm for mining a set of influential spreaders in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 58-65.
    12. Jackie Krafft & Francesco Quatraro, 2011. "The Dynamics of Technological Knowledge: From Linearity to Recombination," Chapters, in: Cristiano Antonelli (ed.), Handbook on the Economic Complexity of Technological Change, chapter 7, Edward Elgar Publishing.
    13. Zhou, Jing & Li, Wei & Wang, Jiaxin & Ding, Shuai & Xia, Chengyi, 2019. "Default prediction in P2P lending from high-dimensional data based on machine learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    14. Giulia Masi & Giorgio Ricchiuti, 2020. "From FDI network topology to macroeconomic instability," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 15(1), pages 133-158, January.
    15. Guilherme Ferraz de Arruda & Giovanni Petri & Pablo Martin Rodriguez & Yamir Moreno, 2023. "Multistability, intermittency, and hybrid transitions in social contagion models on hypergraphs," Nature Communications, Nature, vol. 14(1), pages 1-15, December.
    16. repec:hal:wpspec:info:hdl:2441/f6h8764enu2lskk9p5487a6cm is not listed on IDEAS
    17. Nie, Yanyi & Li, Wenyao & Pan, Liming & Lin, Tao & Wang, Wei, 2022. "Markovian approach to tackle competing pathogens in simplicial complex," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    18. Gomez, Daniel & Gonzalez-Aranguena, Enrique & Manuel, Conrado & Owen, Guillermo & del Pozo, Monica & Tejada, Juan, 2003. "Centrality and power in social networks: a game theoretic approach," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 27-54, August.
    19. Jackie Krafft & Francesco Quatraro & Pier Paolo Saviotti, 2011. "The knowledge-base evolution in biotechnology: a social network analysis," Economics of Innovation and New Technology, Taylor & Francis Journals, vol. 20(5), pages 445-475.
    20. Dixit, Shiv & Subramanian, Krishnamurthy, 2020. "Bank Coordination and Monetary Transmission: Evidence from India," MPRA Paper 103169, University Library of Munich, Germany.
    21. Keliger, Dániel & Horváth, Illés, 2023. "Accuracy criterion for mean field approximations of Markov processes on hypergraphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:382:y:2020:i:c:s0096300320302976. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.