In this paper, we proposed a novel two-stage optimization method for network community partition, which is based on inherent network structure information. The introduced optimization approach utilizes the new network centrality measure of both links and vertices to construct the key affinity description of the given network, where the direct similarities between graph nodes or nodal features are not available to obtain the classical affinity matrix. Indeed, such calculated network centrality information presents the essential structure of network, hence, the proper measure for detecting network communities, which also introduces a `confidence' criterion for referencing new labeled benchmark nodes. For the resulted challenging combinatorial optimization problem of graph clustering, the proposed optimization method iteratively employs an efficient convex optimization algorithm which is developed based under a new variational perspective of primal and dual. Experiments over both artificial and real-world network datasets demonstrate that the proposed optimization strategy of community detection significantly improves result accuracy and outperforms the state-of-the-art algorithms in terms of accuracy and reliability.