Title: Rich-Club Ordering and the Dyadic Effect: Two Interrelated Phenomena,
Abstract: Rich-club ordering and the dyadic effect are two phenomena observed in
complex networks that are based on the presence of certain substructures
composed of specific nodes. Rich-club ordering represents the tendency of
highly connected and important elements to form tight communities with other
central elements. The dyadic effect denotes the tendency of nodes that share a
common property to be much more interconnected than expected. In this study, we
consider the interrelation between these two phenomena, which until now have
always been studied separately. We contribute with a new formulation of the
rich-club measures in terms of the dyadic effect. Moreover, we introduce
certain measures related to the analysis of the dyadic effect, which are useful
in confirming the presence and relevance of rich-clubs in complex networks. In
addition, certain computational experiences show the usefulness of the
introduced quantities with regard to different classes of real networks.