Identifying robust features of community structure in complex networks

Network science has presented community detection as a valuable tool for revealing functional modules in complex systems rooted in the wiring architectures of complex networks. The varying procedures of community detection can produce, however, divisions of a network into communities that vary considerably in structure but are deemed to be of similar merit. This is especially problematic when the network is constructed on uncertain data, since small changes to the network's configuration can cause radically different structures to be detected. To reconcile with the ambiguity in interpreting degenerate network partitions as representations of the underlying system function, we introduce a recursive significance clustering scheme that identifies the subsets of nodes having stable joint community assignments under network perturbation. These robust node groups are referred to here as cores, and represent well-supported features of network structure as distinct from the nodes with unstable community assignments. We show that cores characterize the variability inherent to nonoverlapping community structure in networks and are cohesive under temporal evolution of the network.