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

Joseph T. Lizier1,2,*, Fatihcan M. Atay1,†, and Jürgen Jost1,3,‡

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

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

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.

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Outline

Information

Phys. Rev. E 86, 026110– Published 15 August, 2012
  • Received 29 November 2011

©2012 American Physical Society

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