Exploring Hubs and Overlapping Nodes Interactions in Modular Complex Networks

Abstract

In real-world networks, nodes are usually organized into modules or communities of densely connected nodes. In situations where nodes can belong to multiple communities we say that the communities overlap, and the nodes shared by more than one community are called the overlapping nodes. This occurs especially in social networks where an individual belongs to various social groups and organizations such as working circles, family, friendship or virtual groups on the Internet. Complex networks are known to have a heavy tail degree distribution. Indeed, they are organized with a vast majority of nodes with few interactions and a small set of highly connected nodes called hubs. In this paper, our goal is to study the relationship between the overlapping nodes and the hubs. Indeed, we suspect that the hubs are in the vicinity of the overlapping nodes. If this assumption is confirmed, it gives a new perspective on how the communities are organized and of the crucial importance of the overlapping nodes. In an attempt to investigate the ubiquity of this property, we perform series of experiments on various real-world networks with overlapping community structure. Results show that the hubs represent always a large proportion of the one-step neighbors of overlapping nodes. These results may have implications in various contexts. For example, searching for the hubs in large networks can be done starting from the overlapping nodes. Furthermore, this study may also provide new directions for designing new community detection algorithms. INDEX TERMS Complex networks, community structure, overlapping nodes, hubs.

Extracting backbones in weighted modular complex networks

“…These results are consistent with the findings of a previous study 53 showing that the overlapping nodes are neighbors of the highly connected nodes of the network. Therefore, the overlapping nodes ego backbones and the overlapping nodes and hubs backbones preserve just about the same set of nodes.…”

“…Results with a single community detection algorithm are reported. Indeed, previous results using alternative community detection algorithm have shown that the influence of the community detection algorithm is limited, and that the community structures uncovered are generally quite consistent 53 .…”

“…Rather than reporting results on the influence of the community detection algorithm on these parameters, we recall the main findings. For more details, the reader can refer to 53 . In this previous study, results of extensive experiments using three community detection algorithms (Demon, an Improved version of LFM, SLPA) on a number of empirical networks of various origin are reported.…”

“…We expect that the overlapping nodes ego backbone is a good approximation of the overlapping nodes and hubs backbone. Indeed, in a previous study 53 , it has been shown that the overlapping nodes are neighbors with a high number of the top connected nodes. Therefore, this backbone should preserve very relevant information from the original network without looking for the hubs that are supposed to belong to the overlapping nodes neighborhood.…”

“…For instance, if we consider a network of actors, the actors may play in films of different genres (comedy, musical, adventure, action, etc). While there is a great deal of works exploiting the modular structure of real-world networks [52][53][54][55][56][57][58][59][60][61][62][63][64] , and despite the ubiquity of this property, up to now, it is ignored in the filter-based backbone extraction approach. This article closes that gap.…”