Enumerating Communities for a Deeper Understanding of Community Finding

Often new insights and advancements are made by a detailed study of the problem and the solution space. The area of community finding has had many algorithms proposed recently, but to our knowledge there have not been any detailed studies of the solution space. In this paper, we present two algorithms for enumerating and unranking the possible valid community assignments for a network. To demonstrate the value of our algorithms, we also present some interesting insights gained by examining the solution space of some small networks.