We propose a visual and interactive method for discovering distinct groups of nodes in a network using a user-selected set of node properties computed from the network structure. The user's input on the visual separation of nodes in random 2D projections of a high-dimensional node property space is systematically analyzed to divide the nodes into distinct groups, the number of which is selected by the user interactively. The discovered groups are then examined to reveal their distinguishing characteristics. Our method is capable of discovering communities structures, k-partite structures, or any other structures in which the groups can be distinguished by a combination of node properties. We demonstrate that our method can effectively find and characterize a variety of group structures in model and real-world networks.