Information Flow in a Model of Policy Diffusion: An Analytical Study

Networks are pervasive across science and engineering, but seldom do we precisely know their topology. The information-theoretic notion of transfer entropy has been recently proposed as a potent means to unveil connectivity patterns underlying collective dynamics of complex systems. By pairwise comparing time series of units in the network, transfer entropy promises to determine whether the units are connected or not. Despite considerable progress, our understanding of transfer entropy-based network reconstruction largely relies on computer simulations, which hamper the precise and systematic assessment of the accuracy of the approach. In this paper, we present an analytical study of the information flow in a network model of policy diffusion, thereby establishing closed-form expressions for the transfer entropy between any pair of nodes. The model consists of a finite-state ergodic Markov chain, for which we compute the joint probability distribution in the stationary limit. Our analytical results offer a compelling evidence for the potential of transfer entropy to assist in the process of network reconstruction, clarifying the role and extent of tenable confounds associated with spurious connections between nodes.