An equation-free approach to coarse-graining the dynamics of networks

Katherine A. Bold, Karthikeyan Rajendran, Balázs Ráth, Ioannis G. Kevrekidis

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

We propose and illustrate an approach to coarse-graining the dynamics of evolving networks, i.e., networks whose connectivity changes dynamically. The approach is based on the equation-free framework: short bursts of detailed network evolution simulations are coupled with lifting and restriction operators that translate between actual network realizations and their appropriately chosen coarse observables. This framework is used here to accelerate temporal simulations through coarse projective integration, and to implement coarse-grained fixed point algorithms through matrix-free Newton-Krylov. The approach is illustrated through a very simple network evolution example, for which analytical approximations to the coarse-grained dynamics can be independently obtained, so as to validate the computational results. The scope and applicability of the approach, as well as the issue of selection of good coarse observables are discussed.

Original languageEnglish (US)
Pages (from-to)111-134
Number of pages24
JournalJournal of Computational Dynamics
Volume1
Issue number1
DOIs
StatePublished - Jun 1 2014

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Computational Mathematics

Keywords

  • Coarsegraining
  • Complex networks
  • Equation-free approach
  • Graph limits
  • Network evolution

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