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Critical Phenomena in Complex Networks: from Scale-free to Random Networks | | Alexander I. Nesterov
; Pablo Héctor Mata Villafuerte
; | | Date: |
5 Aug 2020 | | Abstract: | Within the conventional statistical physics framework, we study critical
phenomena in a class of network models with hidden variables controlling links
between pairs of nodes. We find analytical expressions for the average node
degree, the expected number of edges, and the Landau and Helmholtz free
energies as a function of the temperature and number of nodes. We show that the
network’s temperature is a parameter that controls the transition from
unconnected graphs to power-degree (scale-free) and random graphs. With
increasing temperature, the degree distribution is changed from power-degree,
for lower temperatures, to a Poisson-like distribution for high temperatures.
We also show that phase transition in the sparse networks leads to the
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. | | Source: | arXiv, 2008.02319 | | Services: | Forum | Review | PDF | Favorites | |
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