Information storage, loop motifs, and clustered structure in complex networks

Joseph T. Lizier, Fatihcan M. Atay, and Jürgen Jost

Phys. Rev. E 86, 026110 – Published 15 August 2012

Abstract

We use a standard discrete-time linear Gaussian model to analyze the information storage capability of individual nodes in complex networks, given the network structure and link weights. In particular, we investigate the role of two- and three-node motifs in contributing to local information storage. We show analytically that directed feedback and feedforward loop motifs are the dominant contributors to information storage capability, with their weighted motif counts locally positively correlated to storage capability. We also reveal the direct local relationship between clustering coefficient(s) and information storage. These results explain the dynamical importance of clustered structure and offer an explanation for the prevalence of these motifs in biological and artificial networks.

Received 29 November 2011

DOI:https://doi.org/10.1103/PhysRevE.86.026110

Authors & Affiliations

Joseph T. Lizier^1,2,*, Fatihcan M. Atay^1,†, and Jürgen Jost^1,3,‡

¹Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany
²CSIRO Information and Communications Technology Centre, P. O. Box 76, Epping, New South Wales 1710, Australia
³Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA

^*lizier@mis.mpg.de
^†fatay@mis.mpg.de
^‡jjost@mis.mpg.de

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Vol. 86, Iss. 2 — August 2012

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Physical Review E

covering statistical, nonlinear, biological, and soft matter physics