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What does the informational complexity of dynamical networked systems tell usabout intrinsic mechanisms and functions of these complex systems? Recentcomplexity measures such as integrated information have sought tooperationalize this problem taking a whole-versus-parts perspective, whereinone explicitly computes the amount of information generated by a network as awhole over and above that generated by the sum of its parts during statetransitions. While several numerical schemes for estimating network integratedinformation exist, it is instructive to pursue an analytic approach thatcomputes integrated information as a function of network weights. Ourformulation of integrated information uses a Kullback-Leibler divergencebetween the multi-variate distribution on the set of network states versus thecorresponding factorized distribution over its parts. Implementing stochasticGaussian dynamics, we perform computations for several prototypical networktopologies. Our findings show increased informational complexity nearcriticality, which remains consistent across network topologies. Spectraldecomposition of the system's dynamics reveals how informational complexity isgoverned by eigenmodes of both, the network's covariance and adjacencymatrices. We find that as the dynamics of the system approach criticality, highintegrated information is exclusively driven by the eigenmode corresponding tothe leading eigenvalue of the covariance matrix, while sub-leading modes getsuppressed. The implication of this result is that it might be favorable forcomplex dynamical networked systems such as the human brain or communicationsystems to operate near criticality so that efficient information integrationmight be achieved.

Spectral Modes of Network Dynamics Reveal Increased Informational Complexity Near Criticality