AdaSim: A Recursive Similarity Measure in Graphs

In the literature, various link-based similarity measures such as Adamic/Adar (in short Ada), SimRank, and random walk with restart (RWR) have been proposed. Contrary to SimRank and RWR, Ada is a non-recursive measure, which exploits the local graph structure in similarity computation. Motivated by Ada's promising results in various graph-related tasks, along with the fact that SimRank is a recursive generalization of the co-citation measure, in this paper, we propose AdaSim, a recursive similarity measure based on the Ada philosophy. Our AdaSim provides identical accuracy to that of Ada on the first iteration and it is applicable to both directed and undirected graphs. To accelerate our iterative form, we also propose a matrix form that is dramatically faster while providing the exact AdaSim scores. We conduct extensive experiments with five real-world datasets to evaluate both the effectiveness and efficiency of our AdaSim in comparison with those of existing similarity measures and graph embedding methods in the task of similarity computation of nodes. Our experimental results show that 1) AdaSim significantly improves the effectiveness of Ada and outperforms other competitors, 2) its efficiency is comparable to that of SimRank* while being better than the others, 3) AdaSim is not sensitive to the parameter tuning, and 4) similarity measures are better than embedding methods to compute similarity of nodes.