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 aims at detecting granular overlaps. The clique optimization method is a fine grain scale approach. Each granular overlap is a node connected to distinct communities and it is highly connected to each community. Fuzzy detection is at a coarser grain scale and aims at identifying modular overlaps. Modular overlaps represent groups of nodes that have high com- munity membership degrees with several communities. A modular overlap is itself a possible cluster/sub-community. 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.