论文标题
从网络特征值中找到电阻距离和特征向量的中心性
Finding the Resistance Distance and Eigenvector Centrality from the Network's Eigenvalues
论文作者
论文摘要
有不同的措施来对网络数据集进行分类，这些数据集取决于问题，取决于问题。例如，分别在揭示生态途径和分化阿尔茨海默氏病患者的生物医学图像方面已经成功地揭示了抗性距离和特征向量的中心度度量。电阻距离衡量网络的任何两个节点之间的有效距离，考虑到它们之间的所有可能最短路径，而特征向量中心性测量了网络中每个节点的相对重要性。但是，这两种措施都需要知道网络的特征值和特征向量 - 特征向量是计算上要求更高的任务。在这里，我们表明我们只能使用特征值光谱即可密切近似这两个度量，在这里我们通过在元素电阻电路和范式网络模型（随机和小世界网络）上实验来说明这一点。我们的结果得到了分析推导的支持，表明在所有情况下，在电阻距离都可以密切近似的情况下，特征向量的中心性均可以完美匹配。我们的基本方法是基于Denton，Parke，Tao和Zhang [Arxiv：1908.03795（2019）]的工作，该方法不受限制地对这些拓扑措施进行了不受限制，并且可以应用于需要计算特征vectors的大多数问题。
There are different measures to classify a network's data set that, depending on the problem, have different success. For example, the resistance distance and eigenvector centrality measures have been successful in revealing ecological pathways and differentiating between biomedical images of patients with Alzheimer's disease, respectively. The resistance distance measures the effective distance between any two nodes of a network taking into account all possible shortest paths between them and the eigenvector centrality measures the relative importance of each node in the network. However, both measures require knowing the network's eigenvalues and eigenvectors -- eigenvectors being the more computationally demanding task. Here, we show that we can closely approximate these two measures using only the eigenvalue spectra, where we illustrate this by experimenting on elemental resistor circuits and paradigmatic network models -- random and small-world networks. Our results are supported by analytical derivations, showing that the eigenvector centrality can be perfectly matched in all cases whilst the resistance distance can be closely approximated. Our underlying approach is based on the work by Denton, Parke, Tao, and Zhang [arXiv:1908.03795 (2019)], which is unrestricted to these topological measures and can be applied to most problems requiring the calculation of eigenvectors.
