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Tuning the overlap and the cross-layer correlations in two-layer networks: Application to a susceptible-infectious-recovered model with awareness dissemination

David Juher and Joan Saldaña
Phys. Rev. E 97, 032303 – Published 9 March 2018

Abstract

We study the properties of the potential overlap between two networks A,B sharing the same set of N nodes (a two-layer network) whose respective degree distributions pA(k),pB(k) are given. Defining the overlap coefficient α as the Jaccard index, we prove that α is very close to 0 when A and B are random and independently generated. We derive an upper bound αM for the maximum overlap coefficient permitted in terms of pA(k), pB(k), and N. Then we present an algorithm based on cross rewiring of links to obtain a two-layer network with any prescribed α inside the range (0,αM). A refined version of the algorithm allows us to minimize the cross-layer correlations that unavoidably appear for values of α beyond a critical overlap αc<αM. Finally, we present a very simple example of a susceptible-infectious-recovered epidemic model with information dissemination and use the algorithms to determine the impact of the overlap on the final outbreak size predicted by the model.

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  • Received 29 November 2017

DOI:https://doi.org/10.1103/PhysRevE.97.032303

©2018 American Physical Society

Physics Subject Headings (PhySH)

Networks

Authors & Affiliations

David Juher*

  • Department of IMAE, Universitat de Girona, Girona 17003, Catalonia, Spain

Joan Saldaña

  • Department of IMAE, Universitat de Girona, Girona 17703, Catalonia, Spain and Department of Electrical and Computer Engineering, Kansas State University, Manhattan, Kansas 66506, USA

  • *david.juher@udg.edu
  • joan.saldana@udg.edu

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Issue

Vol. 97, Iss. 3 — March 2018

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