Modularity measure of networks with overlapping communities

In this paper we introduce a non-fuzzy measure which has been designed to rank the partitions of a network's nodes into overlapping communities. Such a measure can be useful for both quantifying clusters detected by various methods and during finding the overlapping community structure by optimization methods. The theoretical problem referring to the separation of overlapping modules is discussed, and an example for possible applications is given as well. Copyright (C) EPLA, 2010