Information parity in complex networks

A growing interest in complex networks theory results in an ongoing demand for new analytical tools. We propose a novel quantity based on information theory that provides a new perspective for a better understanding of networked systems: Termed ”information parity”, it quantifies the consonance of influence among nodes with respect to the whole network architecture. Considering the statistics of geodesic distances, information parity assesses how similarly a pair of nodes can influence and be influenced by the network. This allows us to quantify the access of information gathered by the nodes. To demonstrate the method's potential, we evaluate a social network and human brain networks. Our results indicate that emerging phenomena like an ideological orientation of nodes in social networks can be detected by their information parities. We also show the potential of information parity to identify central network regions in structural brain networks placed near mid-sagittal plane. We find that functional networks have, on average, greater information parity for inter-hemispheric homologous regions in comparison to the whole network. This property of information parity suggests that the functional correlations between regional activities could be explained by the symmetry of their overall influences on the whole brain.