  It has been shown that the communities of complex networks often overlap with
each other. However, there is no effective method to quantify the overlapping
community structure. In this paper, we propose a metric to address this
problem. Instead of assuming that one node can only belong to one community,
our metric assumes that a maximal clique only belongs to one community. In this
way, the overlaps between communities are allowed. To identify the overlapping
community structure, we construct a maximal clique network from the original
network, and prove that the optimization of our metric on the original network
is equivalent to the optimization of Newman's modularity on the maximal clique
network. Thus the overlapping community structure can be identified through
partitioning the maximal clique network using any modularity optimization
method. The effectiveness of our metric is demonstrated by extensive tests on
both the artificial networks and the real world networks with known community
structure. The application to the word association network also reproduces
excellent results.
