Overlapping Communities Explain Core–Periphery Organization of Networks

Networks provide a powerful way to study complex systems of interacting objects. Detecting network communities-groups of objects that often correspond to functional modules-is crucial to understanding social, technological, and biological systems. Revealing communities allows for analysis of system properties that are invisible when considering only individual objects or the entire system, such as the identification of module boundaries and relationships or the classification of objects according to their functional roles. However, in networks where objects can simultaneously belong to multiple modules at once, the decomposition of a network into overlapping communities remains a challenge. Here we present a new paradigm for uncovering the modular structure of complex networks, based on a decomposition of a network into any combination of overlapping, nonoverlapping, and hierarchically organized communities. We demonstrate on a diverse set of networks coming from a wide range of domains that our approach leads to more accurate communities and improved identification of community boundaries. We also unify two fundamental organizing principles of complex networks: the modularity of communities and the commonly observed core-periphery structure. We show that dense network cores form as an intersection of many overlapping communities. We discover that communities in social, information, and food web networks have a single central dominant core while communities in protein-protein interaction (PPI) as well as product copurchasing networks have small overlaps and form many local cores.