Link prediction is a fundamental challenge in network science. Among various methods, similarity-based algorithms are popular for their simplicity, interpretability, high efficiency and good performance. In this paper, we show that the most elementary local similarity index Common Neighbor (CN) can be linearly decomposed by eigenvectors of the adjacency matrix of the target network, with each eigenvector’s contribution being proportional to the square of the corresponding eigenvalue. As in many real networks, there is a huge gap between the largest eigenvalue and the second largest eigenvalue, the CN index is thus dominated by the leading eigenvector and much useful information contained in other eigenvectors may be overlooked. Accordingly, we propose a parameter-free algorithm that ensures the contributions of the leading eigenvector and the secondary eigenvector the same. Extensive experiments on real networks demonstrate that the prediction performance of the proposed algorithm is remarkably better than well-performed local similarity indices in the literature. A further proposed algorithm that can adjust the contribution of leading eigenvector shows the superiority over state-of-the-art algorithms with tunable parameters for its competitive accuracy and lower computational complexity.

链路预测是网络科学中的一项基本挑战。在各种方法中，基于相似性的算法因其简单、可解释、高效和良好的性能而广受欢迎。在本文中，我们展示了最基本的局部相似性指标Common Neighbor (CN) 可以通过目标网络的邻接矩阵的特征向量进行线性分解，每个特征向量的贡献与相应特征值的平方成正比。由于在许多实际网络中，最大特征值和第二大特征值之间存在巨大差距，因此 CN 索引以领先的特征向量为主，而其他特征向量中包含的许多有用信息可能会被忽略。因此，我们提出了一种无参数算法，以确保前导特征向量和次要特征向量的贡献相同。在真实网络上的大量实验表明，所提出算法的预测性能明显优于文献中表现良好的局部相似性指数。进一步提出的可以调整领先特征向量贡献的算法显示出优于具有可调参数的最先进算法的优势，因为其具有竞争力的准确性和较低的计算复杂度。