Rich-club phenomenon across complex network hierarchies

The “rich-club phenomenon” in complex networks is characterized when nodes of higher degree are more interconnected than nodes with lower degree. The presence of this phenomenon may indicate several interesting high-level network properties, such as tolerance to hub failures. Here, the authors investigate the existence of this phenomenon across the hierarchies of several real-world networks. Their simulations reveal that the presence or absence of this phenomenon in a network does not imply its presence or absence in the network’s successive hierarchies, and that this behavior is even nonmonotonic in some cases.