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To understand the formation, evolution, and function of complex systems, it is crucial to understand the internal organization of their interaction networks. Partly due to the impossibility of visualizing large complex networks, resolving network structure remains a challenging problem. Here we overcome this difficulty by combining the visual pattern recognition ability of humans with the high processing speed of computers to develop an exploratory method for discovering groups of nodes characterized by common network properties, including but not limited to communities of densely connected nodes. Without any prior information about the nature of the groups, the method simultaneously identifies the number of groups, the group assignment, and the properties that define these groups. The results of applying our method to real networks suggest the possibility that most group structures lurk undiscovered in the fast-growing inventory of social, biological, and technological networks of scientific interest.
The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a great variety of complex systems has been successfully described as networks whose interacting
Real networks are finite metric spaces. Yet the geometry induced by shortest path distances in a network is definitely not its only geometry. Other forms of network geometry are the geometry of latent spaces underlying many networks, and the effectiv
Social groups are fundamental building blocks of human societies. While our social interactions have always been constrained by geography, it has been impossible, due to practical difficulties, to evaluate the nature of this restriction on social gro
Individual nodes in evolving real-world networks typically experience growth and decay --- that is, the popularity and influence of individuals peaks and then fades. In this paper, we study this phenomenon via an intrinsic nodal fitness function and
Community identification of network components enables us to understand the mesoscale clustering structure of networks. A number of algorithms have been developed to determine the most likely community structures in networks. Such a probabilistic or