Overlapping-box-covering method for the fractal dimension of complex networks.
Overlapping-box-covering method for the fractal dimension of complex networks.
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DOI：
10.1103/physreve.89.042809
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发表时间：
2014-04
期刊：
影响因子：
--
通讯作者：
Yuanyuan Sun;Yujie Zhao
中科院分区：
文献类型：
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作者：
Yuanyuan Sun;Yujie Zhao
复杂网络的分形性和自相似性已被广泛研究，其关键是如何找到最优解或如何用最少的盒子来拼接网络。分箱复盖法的计算结果具有较大的随机性或误差。在本文中，我们采用重叠盒来平铺整个网络，称为重叠盒覆盖方法。在这种情况下，为了验证它的有效性，我们提出了一个覆盖盒算法，我们首先将其应用到三个确定性网络，然后到四个现实世界的分形网络。前者产生最优或更精确的分形维数，后者最终得到的盒子数量更少，更确定，冗余盒子高达33.3%。实验结果表明，重叠盒覆盖法是可行的，重叠盒的效果优于前一种情况，误差较小。此外，我们得出结论，重叠盒是一个重要的决定因素，以获得最少的盒复杂网络。
The fractality and self-similarity of complex networks have been widely investigated by evaluating the fractal dimension, the crux of which is how to locate the optimal solution or how to tile the network with the fewest boxes. The results yielded by the box-covering method with separated boxes possess great randomness or large errors. In this paper, we adopt the overlapping box to tile the entire network, called the overlapping-box-covering method. In such a case, for verifying its validity, we propose an overlapping-box-covering algorithm; we first apply it to three deterministic networks, then to four real-world fractal networks. It produces optimums or more accurate fractal dimension for the former; the quantities of boxes finally obtained for the latter are fewer and more deterministic, with the redundant box reaching up to 33.3%. The experimental results show that the overlapping-box-covering method is available and that the overlapping box outperforms the previous case, rendering the errors smaller. Moreover, we conclude that the overlapping box is an important determinant to acquire the fewest boxes for complex networks.