This paper proposes a complex network community partitioning (Weighted-Louvain algorithm, WL) algorithm based on edge weights for serious skewed network data. This algorithm can discover the strong relational community in the weak relational network, thus mining the implicit user relationship in the network. The comparison between the experimental results of WL algorithm and Louvain algorithm on different datasets shows that the WL algorithm can find small-scale community structure in the network, and obtain higher resolution as well as higher operational efficiency, which is capable of mining real user relationships implied in the social networks.