Transition from fractal to non-fractal scalings in growing scale-free networks
Transition from fractal to non-fractal scalings in growing scale-free networks
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DOI：
10.1140/epjb/e2008-00299-1
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发表时间：
2008-03
期刊：
影响因子：
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通讯作者：
Zhongzhi Zhang;Shuigeng Zhou;L. Chen;J. Guan
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文献类型：
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作者：
Zhongzhi Zhang;Shuigeng Zhou;L. Chen;J. Guan
真实的网络可以分为两类：分形网络和非分形网络。在这里，我们介绍了两种类型的网络的统一模型。我们的模型网络由一个参数q控制。我们得到的网络的拓扑性质，包括度分布，平均路径长度，直径，分形维数，介数中心分布，这是由参数q控制。有趣的是，通过调整q，网络经历了从分形到非分形的转变，同时表现出从“大”到小世界的交叉。我们的研究对于理解分形网络和非分形网络的演化和相互关系有一定的启示。
Real networks can be classified into two categories: fractal networks and non-fractal networks. Here we introduce a unifying model for the two types of networks. Our model network is governed by a parameterq. We obtain the topological properties of the network including the degree distribution, average path length, diameter, fractal dimensions, and betweenness centrality distribution, which are controlled by parameterq. Interestingly, we show that by adjustingq, the networks undergo a transition from fractal to non-fractal scalings, and exhibit a crossover from ‘large’ to small worlds at the same time. Our research may shed some light on understanding the evolution and relationships of fractal and non-fractal networks.