Issue
EPL
Volume 85, Number 6, March 2009
Article Number 68006
Number of page(s) 6
Section Interdisciplinary Physics and Related Areas of Science and Technology
DOI http://dx.doi.org/10.1209/0295-5075/85/68006
Published online 07 April 2009
EPL, 85 (2009) 68006
DOI: 10.1209/0295-5075/85/68006

Modularity produces small-world networks with dynamical time-scale separation

Raj Kumar Pan and Sitabhra Sinha

The Institute of Mathematical Sciences, C.I.T. Campus - Taramani, Chennai, 600 113 India

rajkp@imsc.res.in
sitabhra@imsc.res.in

received 16 December 2008; accepted in final form 5 March 2009; published March 2009
published online 7 April 2009

Abstract
The functional consequences of local and global dynamics can be very different in natural systems. Many such systems have a network description that exhibits strong local clustering as well as high communication efficiency, often termed as small-world networks (SWN). We show that modular organization in otherwise random networks generically give rise to SWN, with a characteristic time-scale separation between fast intra-modular and slow inter-modular processes. The universality of this dynamical signature, that distinguishes modular networks from earlier models of SWN, is demonstrated by processes as different as spin-ordering, synchronization and diffusion.

PACS
89.75.Hc - Networks and genealogical trees.
05.45.-a - Nonlinear dynamics and chaos.
89.75.Fb - Structures and organization in complex systems.

© EPLA 2009