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| Fractal Analysis of Weighted Networks by a Modified Information Dimension Method |
| HUANG Yi, ZHANG Sheng, DAI Weikai, WANG Shuo, YANG Fang
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| School of Information Engineering, Nanchang Hangkong University, Nanchang 330063, China |
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Abstract The fractal property is considered as the third fundamental topology features of complex networks. Studies on the fractal property of complex networks are of great significance for understanding the structure complexity of the network. The information dimension method is a useful tool to measure the fractal property of complex networks. The existing information dimension method is mainly used to analyze the fractal property of unweighted networks, and it is not fully applicable to analyze the fractal property of weighted networks. In this paper, motivated by the idea of box-covering algorithm for weighted complex networks, a fractal analysis method of weighted networks based on information dimension is proposed. We first apply this method to study the fractal property of a family of constructed “Sierpinski” weighted fractal networks, the results show that the fractal dimension of these networks obtained by the proposed method are very close to its theoretical similarity dimension. Then, we apply the proposed method to study the fractal property of three real-world weighted networks and make a detail comparison with the box-covering algorithm, results demonstrate that the proposed method is effective for the fractal scaling analysis of real-world weighted complex networks.
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Received: 07 March 2018
Published: 09 January 2019
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