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Robustness and modular structure in networks

Published online by Cambridge University Press:  27 July 2015

JAMES P. BAGROW
Affiliation:
Mathematics & Statistics, University of Vermont, Burlington, VT, USA and Center for Complex Network Research, Northeastern University, Boston, MA, USA (e-mail: james.bagrow@uvm.edu)
SUNE LEHMANN
Affiliation:
DTU Informatics, Technical University of Denmark, Kgs Lyngby, Denmark and College of Computer and Information Science, Northeastern University, Boston, MA, USA (e-mail: sljo@dtu.dk)
YONG-YEOL AHN
Affiliation:
School of Informatics & Computing, Indiana University, Bloomington IN, USA and Center for Complex Network Research, Northeastern University, Boston, MA, USA (e-mail: yyahn@indiana.edu)

Abstract

Complex networks have recently attracted much interest due to their prevalence in nature and our daily lives (Vespignani, 2009; Newman, 2010). A critical property of a network is its resilience to random breakdown and failure (Albert et al., 2000; Cohen et al., 2000; Callaway et al., 2000; Cohen et al., 2001), typically studied as a percolation problem (Stauffer & Aharony, 1994; Achlioptas et al., 2009; Chen & D'Souza, 2011) or by modeling cascading failures (Motter, 2004; Buldyrev et al., 2010; Brummitt, et al. 2012). Many complex systems, from power grids and the Internet to the brain and society (Colizza et al., 2007; Vespignani, 2011; Balcan & Vespignani, 2011), can be modeled using modular networks comprised of small, densely connected groups of nodes (Girvan & Newman, 2002). These modules often overlap, with network elements belonging to multiple modules (Palla et al. 2005; Ahn et al. 2010). Yet existing work on robustness has not considered the role of overlapping, modular structure. Here we study the robustness of these systems to the failure of elements. We show analytically and empirically that it is possible for the modules themselves to become uncoupled or non-overlapping well before the network disintegrates. If overlapping modular organization plays a role in overall functionality, networks may be far more vulnerable than predicted by conventional percolation theory.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2015 

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