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We propose a novel stochastic graph matching algorithm based on data-driven Markov Chain Monte Carlo (DDMCMC) sampling technique. The algorithm explores the solution space efficiently and avoid local minima by taking advantage of spectral properties of the given graphs in data-driven proposals. Thus, it enables the graph matching to be robust to deformation and outliers arising from the practical correspondence problems. Our comparative experiments using synthetic and real data demonstrate that the algorithm outperforms the state-of-the-art graph matching algorithms.