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.

Exploring Hubs and Overlapping Nodes Interactions in Modular Complex Networks

“…More recently Kudelka et al [24] presented a new perspective on the problem of group detection bridging the gap between structural and ground-truth communities. Using the non-symmetric structural similarity between pairs of nodes, they introduce an algorithm to detect groups referred as zones.…”

Global and local community memberships for estimating spreading capability of nodes in social networks

“…It also shows that local information on the direct neighbourhood of nodes corresponds to aspects of the global community structure of networks (see Kudelka et al. 2019 ). In addition to that, as opposed to other common local immunisation strategies, our measure does not need any pre-calculated or ground-truth knowledge of the community structure, and instead infers such information using local information only, making it computationally more efficient as well as more applicable to real-world scenarios.…”

A comparative study of overlapping community detection methods from the perspective of the structural properties

“…Currently, many works show that community structure and community detection methods can only be understood if the structural properties of the communities are investigated (Jebabli et al 2018;Yang and Leskovec 2014;Harenberg et al 2014;Kudelka et al 2019), as discussed in "Introduction". One of the main objectives of this work is to investigate if the community structures identified by the methods for overlapping community detection arise from the connections embedded in the network or if they are a mere consequence of the assumptions that the methods make about what is a community structure and the sequence of steps implemented by the methods to obtain this structure.…”

“…Moreover, the definition of what is a community is still far from a consensus as more questions are raised about what properties of complex systems a group of nodes should represent. Despite the difficulty in characterizing the limits of density for the definition of what is a community, some recent works show that structural properties of networks may show very low correlation with the metadata of the nodes, i.e, the functional communities presented in the network (Peel et al 2017;Yang and Leskovec 2014;Harenberg et al 2014;Peixoto 2020;Jebabli et al 2018;Kudelka et al 2019). Thus, when a particular criterion is defined to be optimized as an objective function by a community detection method, it can be considered as an implicit assumption about the characterization of an overlapping community structure (Schaub et al 2017;Peel et al 2017;Jebabli et al 2018).…”

“…In a different perspective, the experiments conducted in this work investigate the structural properties of the overlapping communities identified by the studied methods and the similarity of patterns in the topology of the extracted communities with Ground-Truth communities. The investigation of some structural properties of communities is performed in some works in the literature (Clauset et al 2004;Ravasz et al 2002;Palla et al 2005;Leskovec et al 2010), but more recently it has become clearer the importance of a deep investigation in the topological properties of the community structure identified by community detection (Peel et al 2017;Jebabli et al 2018;Orman et al 2012;Kudelka et al 2019). A similar approach was previously followed by Hric et al (2014), but only considering the disjoint community structure.…”