Geometric explanation of the rich-club phenomenon in complex networks.

The rich club organization (the presence of highly connected hub core in a network) influences many structural and functional characteristics of networks including topology, the efficiency of paths and distribution of load. Despite its major role, the literature contains only a very limited set of models capable of generating networks with realistic rich club structure. One possible reason is that the rich club organization is a divisive property among complex networks which exhibit great diversity, in contrast to other metrics (e.g. diameter, clustering or degree distribution) which seem to behave very similarly across many networks. Here we propose a simple yet powerful geometry-based growing model which can generate realistic complex networks with high rich club diversity by controlling a single geometric parameter. The growing model is validated against the Internet, protein-protein interaction, airport and power grid networks.