The rich-club phenomenon across complex network hierarchies

The so-called rich-club phenomenon in a complex network is characterized when nodes of higher degree (hubs) are better connected among themselves than are nodes with smaller degree. The presence of the rich-club phenomenon may be an indicator of several interesting high-level network properties, such as tolerance to hub failures. Here we investigate the existence of the rich-club phenomenon across the hierarchical degrees of a number of real-world networks. Our simulations reveal that the phenomenon may appear in some hierarchies but not in others and, moreover, that it may appear and disappear as we move across hierarchies. This reveals the interesting possibility of non-monotonic behavior of the phenomenon; the possible implications of our findings are discussed.