Information parity in complex networks

Abstract: A growing interest in complex networks theory results in an ongoing demand for new analytical tools. We propose a novel measure 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 detects how similar a pair of nodes can influence and be influenced by the network. This allows us to quantify the quality 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 a social network is severely influenced by their information parities. We also show that anatomical brain networks have a greater information parity in inter-hemispheric correspondent regions placed near the sagittal plane. Finally, functional networks have, on average, greater information parity for inter-hemispheric correspondent regions in comparison to the whole network. We find that a pair of regions with high information parity exhibits higher correlation, suggesting that the functional correlations between cortical regions can be partially explained by the symmetry of their overall influences of the whole brain.