A novel graph matching method based on the local and global distance information of the graph nodes

Graph matching is a classical NP-hard problem, and it plays an important role in many applications in computer science. In this paper, we propose an approximate graph matching method. For two graphs to be matched, our method first constructs an association graph with nodes representing the candidate correspondences between the two original graphs. It then constructs an affinity matrix based on the local and global distance information between the original graphs’ nodes. Each element of the matrix represents the mutual consistency of a pair of nodes of the association graph. After simulating random walks on the association graph, a stable quasi-stationary distribution is obtained. With the Hungarian algorithm, our method finally discretizes the distribution to achieve an approximate matching between the two original graphs. Experiments on two commonly used datasets demonstrate the effectiveness of our method on graph matching.