  Community structure analysis is a powerful tool for social networks, which
can simplify their topological and functional analysis considerably. However,
since community detection methods have random factors and real social networks
obtained from complex systems always contain error edges, evaluating the
significance of community structure partitioned is an urgent and important
question. In this paper, integrating the specific characteristics of real
society, we present a novel framework analyzing the significance of social
community specially. The dynamics of social interactions are modeled by
identifying social leaders and corresponding hierarchical structures. Instead
of a direct comparison with the average outcome of a random model, we compute
the similarity of a given node with the leader by the number of common
neighbors. To determine the membership vector, an efficient community detection
algorithm is proposed based on the position of nodes and their corresponding
leaders. Then, using log-likelihood score, the tightness of community can be
derived. Based on the distribution of community tightness, we establish a new
connection between $p$-value theory and network analysis and then get a novel
statistical form significance measure. Finally, the framework is applied to
both benchmark networks and real social networks. Experimental results show
that our work can be used in many fields, such as determining the optimal
number of communities, analyzing the social significance of a given community,
comparing the performance among various algorithms and so on.
