Graph information theoretic measures on functional connectivity networks based on graph-to-signal transform

A wide variety of complex networks arise in multiple disciplines and the study of their structural information is key for the understanding of the underlying systems. Various graph-based information theoretic measures exist, including those accounting for the spectral distribution of graph matrices and those defining distributions on the graph vertices. In this work, we propose to compute graph information theoretic measures of functional connectivity networks based on the normalized power spectrum of graph signals, introducing a new definition of graph entropy and graph divergence. Results from simulated networks show how the proposed methods reflect the structural information of the networks and overcome ambiguities in the current methods. Finally, it is shown how the proposed measures allow the discrimination between conditions from a cognitive control experiment and reflect changes in the network complexity at time intervals corresponding to the emergence of the event-related negativity brain potential.