Statistical mechanics of multiplex networks: entropy and overlap.

By Ginestra Bianconi. Physical review. E, Statistical, nonlinear, and soft matter physics, 2013

300 citations recorded by the source corpus.

There is growing interest in multiplex networks where individual nodes take part in several layers of networks simultaneously. This is the case, for example, in social networks where each individual node has different kinds of social ties or transportation systems where each location is connected to another location by different types of transport. Many of these multiplexes are characterized by a significant overlap of the links in different layers. In this paper we introduce a statistical mechanics framework to describe multiplex ensembles. A multiplex is a system formed by N nodes and M layers of interactions where each node belongs to the M layers at the same time. Each layer α is formed by a network G^{α}. Here we introduce the concept of correlated multiplex ensembles in which the existence of a link in one layer is correlated with the existence of a link in another layer. This implies that a typical multiplex of the ensemble can have a significant overlap of the links in the different layers. Moreover, we characterize microcanonical and canonical multiplex ensembles satisfying respectively hard and soft constraints and we discuss how to construct multiplexes in these ensembles. Finally, we provide the expression for the entropy of these ensembles that can be useful to address different inference problems involving multiplexes.

Subfields: Computational Theory and Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/899cae75263a63c12138909410768d8b220b711b

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In Statistical and Nonlinear Physics

Citations in the corpus

Multilayer networks (2013, background): “Bianconi [45, 227] introduced microcanonical and canonical network ensembles [256, 316] for multiplex networks.”
Mathematical Formulation of Multilayer Networks (2013, unknown): “[23] G.”
Ranking in interconnected multilayer networks reveals versatile nodes (2013, background): “It is important to discuss the difference between the topological structure which represents the core of this study, namely interconnected multilayer networks [4, 5, 6, 7, 8, 9, 10], and other multilayer structures which have been named multiplexes in the past and have been the subject of recent stu”
The statistical physics of real-world networks (2018, background): “More realistic models of correlated multiplexes—in which the existence of a link in one layer is correlated with the existence of a link in another layer—can be generated by constraining the multilink structure of the system [145].”
The structure and dynamics of multilayer networks (2014, background): “The total overlap O between two layers α and β [49,63] is defined as the total number of links that are in common between layer α and layer β:”