Multiple structural transitions in interacting networks

Giacomo Rapisardi, Alex Arenas, Guido Caldarelli, and Giulio Cimini
Phys. Rev. E 98, 012302 – Published 9 July 2018

Abstract

Many real-world systems can be modeled as interconnected multilayer networks, namely, a set of networks interacting with each other. Here, we present a perturbative approach to study the properties of a general class of interconnected networks as internetwork interactions are established. We reveal multiple structural transitions for the algebraic connectivity of such systems, between regimes in which each network layer keeps its independent identity or drives diffusive processes over the whole system, thus generalizing previous results reporting a single transition point. Furthermore, we show that, at first order in perturbation theory, the growth of the algebraic connectivity of each layer depends only on the degree configuration of the interaction network (projected on the respective Fiedler vector), and not on the actual interaction topology. Our findings can have important implications in the design of robust interconnected networked systems, particularly in the presence of network layers whose integrity is more crucial for the functioning of the entire system. We finally show results of perturbation theory applied to the adjacency matrix of the interconnected network, which can be useful to characterize percolation processes on such systems.

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  • Received 28 February 2018

DOI:https://doi.org/10.1103/PhysRevE.98.012302

©2018 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsNetworks

Authors & Affiliations

Giacomo Rapisardi1,*, Alex Arenas2, Guido Caldarelli1,3, and Giulio Cimini1,3

  • 1IMT School for Advanced Studies, 55100 Lucca, Italy
  • 2Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain
  • 3Istituto dei Sistemi Complessi (ISC)-CNR, 00185-Rome, Italy

  • *giacomo.rapisardi@imtlucca.it

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Issue

Vol. 98, Iss. 1 — July 2018

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