分形维数是度量复杂网络分形特性的最重要的一个指标,其中体积维数被广泛应用于度量无权网络的分形特性。沿着无权网络体积维数的思想进一步考虑,以在给定盒子长度下覆盖到的节点强度和来定义加权网络体积维中“体积”的概念,提出了基于节点强度的加权网络体积维数,并称这种度量加权网络分形特性的维数为强度体积维。首先,利用强度体积维分析了两类具有规则分形结构的谢尔宾斯基(Sierpinski)加权分形网络和康托三角尘(Cantor Dust)加权分形网络,结果表明强度体积维数的值与理论计算的维数值具有非常小的误差。然后,利用强度体积维分析了3个实际加权网络的分形特性,并将结果与利用盒维数得到的结果进行比较,结果表明强度体积维也能够较好地度量实际加权网络的分形特征。
黄毅
,
张胜
,
戴维凯
,
王硕
,
杨芳
,
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
.
DOI: 10.13306/j.1672-3813.2018.03.006
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.
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