High Integrated Information in Complex Networks Near Criticality

Integrated information has recently been proposed as an information-theoretic measure of a network’s dynamical complexity. It aims to capture the amount of information generated by a network as a whole over and above that generated by the sum of its parts when the network transitions from one dynamical state to another. Several formulations of this measure have been proposed, with numerical schemes for computing network complexity. In this paper, we approach the problem analytically. We compute the integrated information of weighted networks with stochastic dynamics. Our formulation makes use of the Kullback-Leibler divergence between the multi-variate distribution on the set of network states versus the corresponding factorized distribution over its parts. Using Gaussian distributions, we compute analytic results for several prototypical network topologies. Our findings show that operating near the edge of criticality is favorable for a high rate of information integration in complex dynamical networks. This observation is consistent across network topologies. We discuss the implication of these results for biological and communication networks.