From Caesar to Twitter: An Axiomatic Approach to Elites of Social Networks

In many complex networks there is a relatively small group of participants that is well connected and highly influential. In order to understand the whole network and the underlying mechanisms it is very helpful to study the characteristics and the emergence of such a group. Many functional properties are associated with high degree nodes and their interconnectivity patterns (rich-club phenomenon). In this paper we examine structural properties of the x-rich-club of nine existing complex networks, where the x-rich-club is the subgraph induced of the x nodes with the highest degree out of all n nodes in the network. We observe in all networks we analyzed, that a small-sized rich-club containing about √ n nodes forms a dense subgraph which is connected to a significant fraction of the outside nodes, consists mainly of nodes that arrived to the network early, is more symmetric than the whole network and has a much higher induced average degree than the network as a whole.