Role Similarity Metric Based on Spanning Rooted Forest

TL;DR

This paper introduces ForestSim, a novel role similarity metric for network analysis that enables efficient top-k queries on large networks, with proven theoretical properties and scalable algorithms.

Contribution

The paper proposes ForestSim, a new role similarity measure with an efficient top-k search algorithm and an approximate precomputation method, improving scalability and performance.

Findings

ForestSim is admissible and satisfies axiomatic properties.

The top-k search runs in O(k) time after precomputation.

Experimental results show ForestSim's efficiency on million-scale networks.

Abstract

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 $O(\epsilon^{-2}m\log^5{n}\log{\frac{1}{\epsilon}})$ and $O(m\log^3{n})$, respectively. Finally, we conduct extensive experiments on 26 real-world networks. The results show that \textsf{ForestSim} works efficiently on million-scale networks and achieves comparable performance to the state-of-art methods.