Discovering the hidden community structure is a fundamental problem in network and graph analysis. Several approaches have been proposed to solve this challenging problem. Among them, detecting overlapping communities in a network is a usual way towards understanding the features of networks. In this paper, we propose a novel approach to identify overlapping communities in large complex networks. It makes an original use of a new community model, called k-clique-star, to discover densely connected structures in social interactions. We show that such model allows to ensure a minimum density on the discovered communities and overcomes some weaknesses of some existing cohesive structures. Experimental results demonstrate the effectiveness and efficiency of our overlapping community model in a variety of real graphs