In this thesis, we propose a method of structural analysis for detecting true/false friend links in an Internet social network. By the balance theory in social science and observed user behaviors, we define a graph optimization problem. We examine the computational complexities and develop heuristic algorithms. More importantly, to show the effectiveness of the new model, we perform experiments on random graphs which simulate the user behavior on Internet social networks. We show the precisions/recalls of both true and false edges. The experimental results show that the new model is effective. Besides detecting true/false friend links, we apply our heuristic algorithms to community detection. We experimented on several benchmarks from the real world and show the performance of the proposed method. According to the experimental results, we verify that the proposed method is useful.