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.