Integrated information for large complex networks

How does one quantify dynamic complexity in large stochastic networks? While measures of integrated information serve as a good start to address these issues, all existing versions of the measure have been plagued with normalization ambiguities and combinatorial explosions which has hindered applications to large-scale networks. In this paper, we propose a new version of integrated information which resolves all these problems and brings us a step closer to addressing complexity in large biological networks. We also show that our measure is the only one which accounts for the total integrated information of a network. We apply this measure to prototypical networks and interestingly find the existence of complexity resonances in the solutions, which suggests a new way of looking at the informational spectrum of complex dynamical systems. Finally, as a proof of principle, we compute how much information is integrated by the anatomical connectivity network of the human cerebral cortex.