Link communities reveal multiscale complexity in networks

Top Cited Papers
Publisher Website
Google Scholar
Abstract
Network theory has become pervasive in all sectors of biology, from biochemical signalling patterns to the structure of human societies, but it has proved difficult to identify relevant functional communities because many nodes belong to several overlapping groups at once and are involved in hierarchical structures. Ahn et al., rather than considering nodes combining to form a tree or dendrogram as the natural community structure, suggest that communities of linkage can explain both overlap and hierarchical organization in networks. They use mobile-phone company records, representing the call patterns and locations of millions of users, to show that branches of the hierarchy are geographically correlated at multiple levels (neighbourhood, city and region) while keeping significant overlap. Linkage dendograms of this type are also demonstrated in published data on protein–protein interactions and metabolic networks. Network theory has become pervasive in all sectors of biology, from biochemical signalling to human societies, but identification of relevant functional communities has been impaired by many nodes belonging to several overlapping groups at once, and by hierarchical structures. These authors offer a radically different viewpoint, focusing on links rather than nodes, which allows them to demonstrate that overlapping communities and network hierarchies are two faces of the same issue. Networks have become a key approach to understanding systems of interacting objects, unifying the study of diverse phenomena including biological organisms and human society1,2,3. One crucial step when studying the structure and dynamics of networks is to identify communities4,5: groups of related nodes that correspond to functional subunits such as protein complexes6,7 or social spheres8,9,10. Communities in networks often overlap9,10 such that nodes simultaneously belong to several groups. Meanwhile, many networks are known to possess hierarchical organization, where communities are recursively grouped into a hierarchical structure11,12,13. However, the fact that many real networks have communities with pervasive overlap, where each and every node belongs to more than one group, has the consequence that a global hierarchy of nodes cannot capture the relationships between overlapping groups. Here we reinvent communities as groups of links rather than nodes and show that this unorthodox approach successfully reconciles the antagonistic organizing principles of overlapping communities and hierarchy. In contrast to the existing literature, which has entirely focused on grouping nodes, link communities naturally incorporate overlap while revealing hierarchical organization. We find relevant link communities in many networks, including major biological networks such as protein–protein interaction6,7,14 and metabolic networks11,15,16, and show that a large social network10,17,18 contains hierarchically organized community structures spanning inner-city to regional scales while maintaining pervasive overlap. Our results imply that link communities are fundamental building blocks that reveal overlap and hierarchical organization in networks to be two aspects of the same phenomenon.