Approximate Matching of Neighborhood Subgraphs — An Ordered String Graph Levenshtein Method

Abstract

Given that exact pair-wise graph matching has a high computational cost, different representational schemes and matching methods have been devised in order to make matching more efficient. Such methods include representing the graphs as tree structures, transforming the structures into strings and then calculating the edit distance between those strings. However many coding schemes are complex and are computationally expensive. In this paper, we present a novel coding scheme for unlabeled graphs and perform some empirical experiments to evaluate its precision and cost for the matching of neighborhood subgraphs in online social networks. We call our method OSG-L (Ordered String Graph-Levenshtein). Some key advantages of the pre-processing phase are its simplicity, compactness and lower execution time. Furthermore, our method is able to match both non-isomorphisms (near matches) and isomorphisms (exact matches), also taking into account the degrees of the neighbors, which is adequate for social network graphs.