Approximate Graph Edit Distance Guided by Bipartite Matching of Bags of Walks

The definition of efficient similarity or dissimilarity measures between graphs is a key problem in structural pattern recognition. This problem is nicely addressed by the graph edit distance, which constitutes one of the most flexible graph dissimilarity measure in this field. Unfortunately, the computation of an exact graph edit distance is known to be exponential in the number of nodes. In the early beginning of this decade, an efficient heuristic based on a bipartite assignment algorithm has been proposed to find efficiently a suboptimal solution. This heuristic based on an optimal matching of nodes’ neighborhood provides a good approximation of the exact edit distance for graphs with a large number of different labels and a high density. Unfortunately, this heuristic works poorly on unlabeled graphs or graphs with a poor diversity of neighborhoods. In this work we propose to extend this heuristic by considering a mapping of bags of walks centered on each node of both graphs.