Role Similarity Metric Based on Spanning Rooted Forest
This work addresses a bottleneck in network analysis for researchers and practitioners by providing a more scalable solution for role similarity queries, though it is incremental as it builds on existing axiomatic properties.
The paper tackles the problem of efficiently computing role similarity metrics for large networks by proposing ForestSim, a new metric based on spanning rooted forests, which reduces precomputation time and space complexity and enables top-k queries in O(k) time, achieving comparable performance to state-of-the-art methods on million-scale networks.
As a fundamental issue in network analysis, structural node similarity has received much attention in academia and is adopted in a wide range of applications. Among these proposed structural node similarity measures, role similarity stands out because of satisfying several axiomatic properties including automorphism conformation. Existing role similarity metrics cannot handle top-k queries on large real-world networks due to the high time and space cost. In this paper, we propose a new role similarity metric, namely \textsf{ForestSim}. We prove that \textsf{ForestSim} is an admissible role similarity metric and devise the corresponding top-k similarity search algorithm, namely \textsf{ForestSimSearch}, which is able to process a top-k query in $O(k)$ time once the precomputation is finished. Moreover, we speed up the precomputation by using a fast approximate algorithm to compute the diagonal entries of the forest matrix, which reduces the time and space complexity of the precomputation to $O(ε^{-2}m\log^5{n}\log{\frac{1}ε})$ and $O(m\log^3{n})$, respectively. Finally, we conduct extensive experiments on 26 real-world networks. The results show that \textsf{ForestSim} works efficiently on million-scale networks and achieves comparable performance to the state-of-art methods.