This paper proposes a weighted-graph based hierarchical community detection approach, which defines the community structure with the use of graph partition. With the pre-defined structure, a novel parallel social network community discovery algorithm (P-SNCD for short) is designed. P-SNCD algorithm avoids the disadvantage of traditional modularity based methods, which tend to discover communities of similar scales. Moreover, it can efficiently mine communities in parallel with the CPU scale of O(hmn) or O(hn²) and time complexity of O(logn), where h represents the density of the communities, m represents the total number of links and n represents the total number of nodes. Compared to the most of the existing methods, P-SNCD algorithm requires a few input parameters makes it even more practical. The accuracy and effectiveness of our algorithm is guaranteed by sufficient empirical studies in the later sections.