https://doi.org/10.1140/epjb/s10051-023-00612-0
Regular Article - Statistical and Nonlinear Physics
Critical phenomena in complex networks: from scale-free to random networks
Departamento de Física, CUCEI, Universidad de Guadalajara, Blvd. Marcelino García Barragán 1421, esq. Calzada Olímpica, 44430, Guadalajara, Jalisco, Mexico
Received:
31
December
2022
Accepted:
17
October
2023
Published online:
2
November
2023
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.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjb/s10051-023-00612-0.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
