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.

节点邻近估计研究节点之间的结构相似性，并且是网络分析的关键问题。它可以作为节点推荐任务存在，并且是其他图挖掘技术的基础。尽管离散时间量子行走（DTQW）是一种很有前途的，具有独特特征的新技术，已广泛用于许多图形挖掘问题中，例如图形同构和图形核，但只有少数工作通过DTQW估计邻近度，从而限制了它的进一步应用。图挖掘中的DTQW。在本文中，我们研究了DTQW进行邻近估计的能力，并提出了QSIM通过DTQW估计节点邻近度。通过分析偏向步行的扩散过程，我们发现了两个对邻近估计有利的影响。递减效果表明，靠近起始节点的节点在扩散过程中通常具有较高的平均概率，这是QSIM的基础。返回效应表明，概率在扩散过程中倾向于停留在起始节点附近，这增强了挖掘局部信息的能力，尤其是在密集连接的结构中。得益于这两种效果，QSIM忠实地揭示了节点接近度，并全面统一了各种类型的节点接近度。QSIM是第一个成熟的基于量子游走的邻近估计方法。大量实验验证了QSIM的有效性，并表明QSIM在节点推荐任务中的性能优于最新方法，大大超过了Refex，Node2vec和Role2vec，最高达到1094。