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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.
Core-periphery networks are structures that present a set of central and densely connected nodes, namely the core, and a set of non-central and sparsely connected nodes, namely the periphery. The rich-club refers to a set in which the highest degree
For many complex networks present in nature only a single instance, usually of large size, is available. Any measurement made on this single instance cannot be repeated on different realizations. In order to detect significant patterns in a real--wor
In this paper we consider the dyadic effect introduced in complex networks when nodes are distinguished by a binary characteristic. Under these circumstances two independent parameters, namely dyadicity and heterophilicity, are able to measure how mu
Ensembles of networks are used as null-models to discriminate network structures. We present an efficient algorithm, based on the maximal entropy method to generate network ensembles defined by the degree sequence and the rich-club coefficient. The m
Identifying the hidden organizational principles and relevant structures of networks representing complex physical systems is fundamental to understand their properties. To this aim, uncovering the structures involving a networks prominent nodes in a