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Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks

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  • Mahendra Piraveenan
  • Mikhail Prokopenko
  • Liaquat Hossain

Abstract

A number of centrality measures are available to determine the relative importance of a node in a complex network, and betweenness is prominent among them. However, the existing centrality measures are not adequate in network percolation scenarios (such as during infection transmission in a social network of individuals, spreading of computer viruses on computer networks, or transmission of disease over a network of towns) because they do not account for the changing percolation states of individual nodes. We propose a new measure, percolation centrality, that quantifies relative impact of nodes based on their topological connectivity, as well as their percolation states. The measure can be extended to include random walk based definitions, and its computational complexity is shown to be of the same order as that of betweenness centrality. We demonstrate the usage of percolation centrality by applying it to a canonical network as well as simulated and real world scale-free and random networks.

Suggested Citation

  • Mahendra Piraveenan & Mikhail Prokopenko & Liaquat Hossain, 2013. "Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks," PLOS ONE, Public Library of Science, vol. 8(1), pages 1-14, January.
    • Handle: RePEc:plo:pone00:0053095
    DOI: 10.1371/journal.pone.0053095
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    2. Belik, Ivan & Jörnsten, Kurt, 2014. "Centrality Computation in Weighted Networks Based on Edge-Splitting Procedure," Discussion Papers 2014/40, Norwegian School of Economics, Department of Business and Management Science.
    3. King, Maia, 2020. "The probabilities of node-to-node diffusion in fixed networks," SocArXiv dfq8y, Center for Open Science.
    4. Feng, Yuhao & Wu, Shufan & Wu, Peixin & Su, Shiliang & Weng, Min & Bian, Meng, 2018. "Spatiotemporal characterization of megaregional poly-centrality: Evidence for new urban hypotheses and implications for polycentric policies," Land Use Policy, Elsevier, vol. 77(C), pages 712-731.
    5. Zádor, Zsófia & Zhu, Zhen & Smith, Matthew & Gorgoni, Sara, 2022. "A weighted and normalized Gould–Fernandez brokerage measure," Greenwich Papers in Political Economy 37794, University of Greenwich, Greenwich Political Economy Research Centre.
    6. Anita Mezzetti & Loic Mar'echal & Dimitri Percia David & William Lacube & S'ebastien Gillard & Michael Tsesmelis & Thomas Maillart & Alain Mermoud, 2022. "TechRank," Papers 2210.07824, arXiv.org.
    7. Mahdi Jalili & Ali Salehzadeh-Yazdi & Yazdan Asgari & Seyed Shahriar Arab & Marjan Yaghmaie & Ardeshir Ghavamzadeh & Kamran Alimoghaddam, 2015. "CentiServer: A Comprehensive Resource, Web-Based Application and R Package for Centrality Analysis," PLOS ONE, Public Library of Science, vol. 10(11), pages 1-8, November.
    8. Mira A. Kantemirova & Mira A. Kantemirova & Zaur L. Dzakoev & Zara R. Alikova & Sergei R. Chedgemov & Sergei R. Chedgemov & Zarina V. Soskieva & Zarina V. Soskieva, 2018. "Percolation approach to simulation of a sustainable network economy structure," Entrepreneurship and Sustainability Issues, VsI Entrepreneurship and Sustainability Center, vol. 5(3), pages 502-513, March.
    9. Sheryl Le Chang & Mahendra Piraveenan & Mikhail Prokopenko, 2019. "The Effects of Imitation Dynamics on Vaccination Behaviours in SIR-Network Model," IJERPH, MDPI, vol. 16(14), pages 1-31, July.
    10. Víctor Martínez & Fernando Berzal & Juan-Carlos Cubero, 2019. "NOESIS: A Framework for Complex Network Data Analysis," Complexity, Hindawi, vol. 2019, pages 1-14, October.
    11. 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).
    12. Nasirian, Farzaneh & Mahdavi Pajouh, Foad & Balasundaram, Balabhaskar, 2020. "Detecting a most closeness-central clique in complex networks," European Journal of Operational Research, Elsevier, vol. 283(2), pages 461-475.
    13. Ullah, Farman & Lee, Sungchang, 2017. "Identification of influential nodes based on temporal-aware modeling of multi-hop neighbor interactions for influence spread maximization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 968-985.
    14. Elhem Ben Fatma & Ezzeddine Ben Mohamed & Léo-Paul Dana & Sami Boudabbous, 2021. "Does entrepreneurs’ psychology affect their business venture success? Empirical findings from North Africa," International Entrepreneurship and Management Journal, Springer, vol. 17(2), pages 921-962, June.
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