Information storage, loop motifs and clustered structure in complex networks

Joseph Lizier, Fatihcan M. Atay, and Jürgen Jost

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Submission date: 24. Oct. 2011 (revised version: November 2011)
Pages: 7
published in: Physical review / E, 86 (2012) 2, art-no. 026110 
DOI number (of the published article): 10.1103/PhysRevE.86.026110
Bibtex
MSC-Numbers: 05C82, 05C38, 94A17
PACS-Numbers: 89.75.Fb, 89.70.Cf, 87.18.Sn, 87.19.lo, 02.10.Ox
Keywords and phrases: information storage, intrinsic computation, complex networks, information theory, neural networks

Abstract:
We use a standard discrete-time linear Gaussian model to analyze information storage capability of individual nodes in complex networks, given network structure and link weights. In particular, we investigate the role of two and three-node motifs in contributing to information storage. We show analytically that directed feedback loops and feedforward loop motifs are the dominant contributors to information storage capability, and show the direct 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.