QSIM: A novel approach to node proximity estimation based on Discrete-time quantum walk

Node proximity estimation studies structural similarity between nodes and is the key issue of network analysis. It can exist as the node recommendation task and is a fundamental basis of other graph mining techniques. Although Discrete-time quantum walk (DTQW), a promising new technique with distinctive characters, is widely used in many graph mining problems such as graph isomorphism and graph kernel, there are only a few works estimating proximity via DTQW, limiting the further application of DTQW in graph mining. In this paper, we study the capability of DTQW for proximity estimation and propose QSIM to estimate node proximity by DTQW. By analyzing the diffusion process of biased walks, we discover two influential effects that are beneficial to proximity estimation. The Diminishing Effect shows that a node close to the starting node can generally have a high average probability during the diffusion process, which serves as the basis of QSIM. The Returning Effect shows the probability has a tendency to stay around the starting node during the diffusion, which enhances the capability for mining local information especially in densely-connected structures. Benefited from the two effects, QSIM faithfully reveals node proximity and comprehensively unifies different kinds of node proximity. QSIM is the first mature quantum-walk-based method for proximity estimation. Extensive experiments validate the effectiveness of QSIM and show that QSIM outperforms state-of-the-art methods in the node recommendation task, significantly surpassing Refex, Node2vec, and Role2vec, by up to 1094.2% in the first-order node proximity and 18.8% in the second-order node proximity.