Overlapping community detection is a popular topic in complex networks. As compared to disjoint community structure, overlapping community structure is more suitable to describe networks at a macroscopic level. Overlaps shared by communities play an important role in combining different communities. In this paper, two methods are proposed to detect overlapping community structure. One is called clique optimization, and the other is named fuzzy detection. Clique optimization detects granular overlaps which are nodes have high togetherness with different communities. Fuzzy detection identified modular overlaps which are groups of nodes shared by several communities. Experimental studies in synthetic networks and real networks show that both methods provide good performances in detecting overlapping nodes but in different views. In addition, a new extension of modularity is introduced for measuring the quality of overlapping community structure.