Abstract：The fractal property is considered as the third fundamental topology features of complex networks. The fractal dimension is the most important measure to characterize the fractal property of complex networks, and the volume dimension is widely used to investigate the fractal property of unweighted networks. In this paper, motivated by the idea of volume dimension of unweighted networks, a new volume dimension measure based on the node strength of weighted networks is proposed. We first apply the proposed method to study the fractal property of two families of weighted fractal networks with regular fractal structures:“Sierpinski” weighted fractal networks and “Cantor dust” weighted fractal networks. The result shows that the numerical fractal dimensions obtained by our method are very close to the theoretical similarity dimension of the network. Then, we use the proposed method to study the fractal property of three more representative real-world weighted networks and the results demonstrate that the proposed method is also effective for the fractal scaling analysis of real-world weighted complex networks.
黄毅, 张胜, 戴维凯, 王硕, 杨芳. 加权网络的体积维数[J]. 复杂系统与复杂性科学, 2018, 15(3): 47-55.
HUANG Yi, ZHANG Sheng, DAI Weikai, WANG Shuo, YANG Fang. The Volume Dimension of Weighted Networks. Complex Systems and Complexity Science, 2018, 15(3): 47-55.
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