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Journal of Computational Dynamics (JCD)
 

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

Pages: 111 - 134, Volume 1, Issue 1, June 2014      doi:10.3934/jcd.2014.1.111

 
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Katherine A. Bold - Program in Applied and Computational Mathematics (PACM), Princeton University, Princeton, New Jersey 08544, United States (email)
Karthikeyan Rajendran - Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, United States (email)
Balázs Ráth - Institute of Mathematics, Budapest University of Technology (BME), H-1111 Budapest, Hungary (email)
Ioannis G. Kevrekidis - Department of Chemical and Biological Engineering, and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, United States (email)

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.

Keywords:  Complex networks, network evolution, equation-free approach, coarsegraining, graph limits.
Mathematics Subject Classification:  Primary: 68U20, 37E25; Secondary: 65Z05.

Received: February 2012;      Revised: October 2012;      Available Online: April 2014.

 References