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.
Information storage, loop motifs, and clustered structure in complex networks
Joseph T. Lizier, Fatihcan M. Atay and Jürgen Jost
Phys. Rev. E 86, 026110 (2012)