Rich-Cores in Networks

Abstract

<div><p>A core comprises of a group of central and densely connected nodes which governs the overall behaviour of a network. It is recognised as one of the key meso-scale structures in complex networks. Profiling this meso-scale structure currently relies on a limited number of methods which are often complex and parameter dependent or require a null model. As a result, scalability issues are likely to arise when dealing with very large networks together with the need for subjective adjustment of parameters. The notion of a <i>rich-club</i> describes nodes which are essentially the hub of a network, as they play a dominating role in structural and functional properties. The definition of a <i>rich-club</i> naturally emphasises high degree nodes and divides a network into two subgroups. Here, we develop a method to characterise a rich-core in networks by theoretically coupling the underlying principle of a rich-club with the escape time of a random walker. The method is fast, scalable to large networks and completely parameter free. In particular, we show that the evolution of the core in World Trade and <i>C. elegans</i> networks correspond to responses to historical events and key stages in their physical development, respectively.</p></div>