A cluster-growing dimension of complex networks: From the view of node closeness centrality

Abstract The cluster-growing method has been widely used to measure the fractal dimension of complex networks. In this method, a seed node is chosen at random and the number of nodes centered at the seed node is calculated. The procedure is then repeated by choosing many seed nodes at random and the total number of nodes within the same fixed length is averaged over the number of seed nodes. In order to improve the statistics, one has to repeat the calculations for sufficient number of seed nodes. However, most real world networks are featured with heterogeneous properties and it is possible that some of the seed nodes are located at the periphery of the networks. In this paper, a modified cluster-growing dimension of complex networks based on closeness centrality of nodes is proposed. By observing and comparing the distinction dimension by choosing the seeds via the proposed method, the original method, the hubs-based method and the CI-based method in a number of networks, we conclude that the dimension of complex networks can be better obtained by choosing the seeds located in the center of complex networks.

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