Graph matching has a wide spectrum of real-world applications and in general is known NP-hard. In many vision tasks, one realistic problem arises for finding the global node mappings across a batch of corrupted weighted graphs. This paper is an attempt to connect graph matching, especially multi-graph matching to the matrix decomposition model and its relevant on-the-shelf convex optimization algorithms. Our method aims to extract the common inliers and their synchronized permutations from disordered weighted graphs in the presence of deformation and outliers. Under the proposed framework, several variants can be derived in the hope of accommodating to other types of noises. Experimental results on both synthetic data and real images empirically show that the proposed paradigm exhibits several interesting behaviors and in many cases performs competitively with the state-of-the-arts.