Due to extensive research on complex networks, fractal analysis with scale invariance is applied to measure the topological structure and self-similarity of complex networks. Fractal dimension can be used to quantify the fractal properties of the complex networks. However, in the existing box covering algorithms, accurately calculating the fractal dimension of complex networks is still an NP-hard problem. Therefore, in this paper, an improved overlapping box covering algorithm is proposed to explore a more accurate and effective method to calculate the fractal dimension of complex networks. Moreover, in order to verify the effectiveness of the algorithm, the improved algorithm is applied to six complex networks, and compared with other algorithms. Finally, the experimental results demonstrate that the improved overlapping box covering algorithm can cover the whole networks with fewer boxes. In addition, the improved overlapping box covering algorithm is a high accuracy and low time complexity method for calculating the fractal dimension of complex networks.

中文翻译：

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复杂网络重叠框覆盖算法的分形分析

由于对复杂网络的广泛研究，具有尺度不变性的分形分析被应用于测量复杂网络的拓扑结构和自相似性。分形维数可用于量化复杂网络的分形特性。然而，在现有的框覆盖算法中，准确计算复杂网络的分形维数仍然是一个NP-hard问题。因此，本文提出了一种改进的重叠框覆盖算法，以探索一种更准确有效的计算复杂网络分形维数的方法。此外，为了验证算法的有效性，将改进算法应用于六个复杂网络，并与其他算法进行比较。最后，实验结果表明，改进的重叠框覆盖算法可以用较少的框覆盖整个网络。此外，改进的重叠框覆盖算法是计算复杂网络分形维数的一种高精度、低时间复杂度的方法。