Title Overlapping Communities Discovery and Improvement

Decomposing a network into communities is one of the most used techniques in network science. Modularity is typically used to measure the goodness of such a decomposition. In this paper we develop a method which allows us to begin with a crisp decomposition (no overlaps) and move to an overlapping decomposition while increasing the modularity. We also show that the same technique can be used to improve existing overlapping decompositions.