Rich-club ordering and the dyadic effect: Two interrelated phenomena

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 that they confirm the presence and relevance of rich-clubs in complex networks and provide certain insights and a baseline for the evaluation of the rich-club size. In addition, certain computational experiences show the usefulness of the introduced quantities with regard to different classes of real networks.