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Critical phenomena in complex networks: from scale-free to random networks

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  • Alexander Nesterov

    (CUCEI, Universidad de Guadalajara)

  • Pablo Héctor Mata Villafuerte

    (CUCEI, Universidad de Guadalajara)

Abstract

Within the conventional statistical physics framework, we study critical phenomena in configuration network models with hidden variables controlling links between pairs of nodes. We obtain analytical expressions for the average node degree, the expected number of edges in the graph, and the Landau and Helmholtz free energies. We demonstrate that the network’s temperature controls the average node degree in the whole network. We also show that phase transition in an asymptotically sparse network leads to fundamental structural changes in the network topology. Below the critical temperature, the graph is completely disconnected; above the critical temperature, the graph becomes connected, and a giant component appears. Increasing temperature changes the degree distribution from power-degree for lower temperatures to a Poisson-like distribution for high temperatures. Our findings suggest that temperature might be an inalienable property of real networks. Graphical abstract

Suggested Citation

  • Alexander Nesterov & Pablo Héctor Mata Villafuerte, 2023. "Critical phenomena in complex networks: from scale-free to random networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(11), pages 1-14, November.
    • Handle: RePEc:spr:eurphb:v:96:y:2023:i:11:d:10.1140_epjb_s10051-023-00612-0
    DOI: 10.1140/epjb/s10051-023-00612-0
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    References listed on IDEAS

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    1. Dorogovtsev, S.N. & Mendes, J.F.F., 2003. "Evolution of Networks: From Biological Nets to the Internet and WWW," OUP Catalogue, Oxford University Press, number 9780198515906, Decembrie.
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    3. Caldarelli, Guido, 2007. "Scale-Free Networks: Complex Webs in Nature and Technology," OUP Catalogue, Oxford University Press, number 9780199211517, Decembrie.
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