The social network is a typical dynamic network. The changes of network nodes, edges and the mapping function over time may cause the restructuring of the network structure, transitioning from one stable state to another stable state, i.e. the emergence of the network structure. This paper first gives the definition of the social network to reach a steady state, and studies the community structure identification method of social network in stable states, inheritance relationship discriminant method for communities in two adjacent states and discriminant method for community stability. Finally, it gives a specific case analysis to describe the community structure evolution and emergence phenomena. © 2013 The Authors. Published by Elsevier B.V.