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As a fundamental issue in network analysis, structural node similarity hasreceived much attention in academia and is adopted in a wide range ofapplications. Among these proposed structural node similarity measures, rolesimilarity stands out because of satisfying several axiomatic propertiesincluding automorphism conformation. Existing role similarity metrics cannothandle top-k queries on large real-world networks due to the high time andspace cost. In this paper, we propose a new role similarity metric, namely\textsf{ForestSim}. We prove that \textsf{ForestSim} is an admissible rolesimilarity metric and devise the corresponding top-k similarity searchalgorithm, namely \textsf{ForestSimSearch}, which is able to process a top-kquery in $O(k)$ time once the precomputation is finished. Moreover, we speed upthe precomputation by using a fast approximate algorithm to compute thediagonal entries of the forest matrix, which reduces the time and spacecomplexity of the precomputation to$O(\epsilon^{-2}m\log^5{n}\log{\frac{1}{\epsilon}})$ and $O(m\log^3{n})$,respectively. Finally, we conduct extensive experiments on 26 real-worldnetworks. The results show that \textsf{ForestSim} works efficiently onmillion-scale networks and achieves comparable performance to the state-of-artmethods.

Role Similarity Metric Based on Spanning Rooted Forest