Jiang Yuanxiang, Li Meng, Fan Ying, Di Zengru
School of Systems Science, Beijing Normal University, Beijing, 100875, China.
Sci Rep. 2021 Mar 11;11(1):5768. doi: 10.1038/s41598-021-85175-9.
Measuring the dissimilarities between networks is a basic problem and wildly used in many fields. Based on method of the D-measure which is suggested for unweighted networks, we propose a quantitative dissimilarity metric of weighted network (WD-metric). Crucially, we construct a distance probability matrix of weighted network, which can capture the comprehensive information of weighted network. Moreover, we define the complementary graph and alpha centrality of weighted network. Correspondingly, several synthetic and real-world networks are used to verify the effectiveness of the WD-metric. Experimental results show that WD-metric can effectively capture the influence of weight on the network structure and quantitatively measure the dissimilarity of weighted networks. It can also be used as a criterion for backbone extraction algorithms of complex network.
衡量网络之间的差异是一个基本问题，并且在许多领域中广泛使用。基于针对无加权网络提出的D-度量方法，我们提出了一种加权网络的定量差异度量（WD-度量）。关键的是，我们构建了加权网络的距离概率矩阵，它可以捕获加权网络的全面信息。此外，我们定义了加权网络的互补图和α中心性。相应地，使用了几个合成网络和真实世界网络来验证WD-度量的有效性。实验结果表明，WD-度量可以有效地捕获权重对网络结构的影响，并定量测量加权网络的差异。它还可以用作复杂网络骨干提取算法的标准。
