Ego-zones: non-symmetric dependencies reveal network groups with large and dense overlaps

Abstract

The existence of groups of nodes with common characteristics and the relationships between these groups are important factors influencing the structures of social, technological, biological, and other networks. Uncovering such groups and the relationships between them is, therefore, necessary for understanding these structures. Groups can either be found by detection algorithms based solely on structural analysis or identified on the basis of more in-depth knowledge of the processes taking place in networks. In the first case, these are mainly algorithms detecting non-overlapping communities or communities with small overlaps. The latter case is about identifying ground-truth communities, also on the basis of characteristics other than only network structure. Recent research into ground-truth communities shows that in real-world networks, there are nested communities or communities with large and dense overlaps which we are not yet able to detect satisfactorily only on the basis of structural network properties.In our approach, we present a new perspective on the problem of group detection using only the structural properties of networks. Its main contribution is pointing out the existence of large and dense overlaps of detected groups. We use the non-symmetric structural similarity between pairs of nodes, which we refer to as dependency, to detect groups that we call zones. Unlike other approaches, we are able, thanks to non-symmetry, accurately to describe the prominent nodes in the zones which are responsible for large zone overlaps and the reasons why overlaps occur. The individual zones that are detected provide new information associated in particular with the non-symmetric relationships within the group and the roles that individual nodes play in the zone. From the perspective of global network structure, because of the non-symmetric node-to-node relationships, we explore new properties of real-world networks that describe the differences between various types of networks.