On The Elite of Social Networks

In many communities there is an elite, a relatively small group of participants that is well connected and highly influential. In order to understand the whole community and the underlying mechanisms it is hence very helpful to study the characteristics and the emergence of the elite. In the past it has been shown that various social networks exhibit surprisingly similar properties, like power law degree distributions, small diameter, many triangles, etc. In this paper we examine the x-elite of nine existing complex networks, where the x-elite consists of the x nodes with the highest degree out of all n nodes in the network. Based on this simple notion of importance, we investigate the structures these nodes form among each other and the rest of the network. We observe, in all networks we analyzed, that a small-sized elite containing about √ n nodes forms a dense subgraph, is connected to a significant fraction of the outside nodes, consists of nodes that arrived to the network early, is more symmetric than the whole network and has a much higher average degree than the network as a whole. We compare these findings to social network models and identify some properties which are not featured by graphs generated by these models. To the best of our knowledge none of the existing models is able to generate networks with the elite properties we observed.