Cumulative merging percolation: A long-range percolation process in networks

Lorenzo Cirigliano, Giulio Cimini, Romualdo Pastor-Satorras, and Claudio Castellano
Phys. Rev. E 105, 054310 – Published 17 May 2022

Abstract

Percolation on networks is a common framework to model a wide range of processes, from cascading failures to epidemic spreading. Standard percolation assumes short-range interactions, implying that nodes can merge into clusters only if they are nearest neighbors. Cumulative merging percolation (CMP) is a percolation process that assumes long-range interactions such that nodes can merge into clusters even if they are topologically distant. Hence, in CMP clusters do not coincide with the topologically connected components of the network. Previous work has shown that a specific formulation of CMP features peculiar mechanisms for the formation of the giant cluster and allows one to model different network dynamics such as recurrent epidemic processes. Here we develop a more general formulation of CMP in terms of the functional form of the cluster interaction range, showing an even richer phase transition scenario with competition of different mechanisms resulting in crossover phenomena. Our analytic predictions are confirmed by numerical simulations.

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  • Received 2 March 2022
  • Revised 22 April 2022
  • Accepted 25 April 2022

DOI:https://doi.org/10.1103/PhysRevE.105.054310

©2022 American Physical Society

Physics Subject Headings (PhySH)

Networks

Authors & Affiliations

Lorenzo Cirigliano1,2, Giulio Cimini3,2, Romualdo Pastor-Satorras4, and Claudio Castellano5,2

  • 1Dipartimento di Fisica, Università Sapienza, Piazzale Aldo Moro 2, 00185 Rome, Italy
  • 2Centro Ricerche Enrico Fermi, Piazza del Viminale 1, 00184 Rome, Italy
  • 3Dipartimento di Fisica and INFN, Università di Roma Tor Vergata, 00133 Rome, Italy
  • 4Departament de Física, Universitat Politècnica de Catalunya, Campus Nord B4, 08034 Barcelona, Spain
  • 5Istituto dei Sistemi Complessi (ISC-CNR), Via dei Taurini 19, 00185 Rome, Italy

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Issue

Vol. 105, Iss. 5 — May 2022

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