ON THE SIGNIFICANCE OF COMMUNITY STRUCTURE IN COMPLEX NETWORKS: ROBUST FEATURES PROVIDE A DESCRIPTION OF VARIABILITY

Abstract

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 problematic when the network is constructed on uncertain data, since small changes to the network's configuration can cause radically different structure to be detected. To reconcile with the ambiguity in interpreting degenerate network partitions as representations of the underlying system function, we put forth the notion of stable "cores" of a network that indicate the features of network structure that are well-supported by the data. We show that cores arrange themselves like building blocks to compose community structure, serving as a description of variability inherent to delineating communities in empirical networks.