-In this paper, consider an algorithm of a community detection taking the diameter of the community as
1.INTRODUCTIONThe term community structure in a network means natural division of the nodes into densely connected subgroups within and between them connection is sparse. By identifying and analysing the community structure of a network, we can understand and characterised the related network and its properties. It is evident that in graph or network, communities are loosely defined and it is not possible to compare the quality of two communities getting by different algorithm of the same graph [1]. By modularity metric, the quality of community structure is measured by Newman[1] , which is based on expected connectivity between nodes .A good high modularity nodes gives good quality community structure. The problem of community detection is that how to define the modularity metric that it may compare the quality of two communities and the partitioning of the nodes that miximizes modularity. Based on the topology of the given network itself not on the expected connectivity, this paper consider a new approach to compute modularity of a community structure. The modularity of a community structure is the average node modularity within it,where the node modularity is defined as the ratio of the number of neighbours of a node v within the same community to the total degree of the node v. So we can say that the modularity value varies between 0 and 1 . By our approach, by joining a node into a community ,it always attempts to maximize its modularity. A node can be addedto a community till that the diameter of the community structure is less than or equal to the predetermined constant k<