最近邻以外复杂网络中长程相关性的量化
Quantifying long-range correlations in complex networks beyond nearest neighbors
摘要：
我们提出了一种波动分析来量化复杂网络中的空间相关性。该方法考虑了网络中沿最短路径的度序列，并将波动量化为时间序列。在这项工作中，Barabasi-Albert（BA）模型，凯莱树在渗流过渡，分形网络模型，和现实世界的网络的例子进行了研究。BA模型的涨落函数呈指数衰减，而Cayley树和分形网络模型的涨落函数呈幂律衰减。分形网络模型包括长程反相关。结果表明，波动指数提供了补充信息的分形维数。
英文摘要：
We propose a fluctuation analysis to quantify spatial correlations in complex networks. The approach considers the sequences of degrees along shortest paths in the networks and quantifies the fluctuations in analogy to time series. In this work, the Barabasi-Albert (BA) model, the Cayley tree at the percolation transition, a fractal network model, and examples of real-world networks are studied. While the fluctuation functions for the BA model show exponential decay, in the case of the Cayley tree and the fractal network model the fluctuation functions display a power-law behavior. The fractal network model comprises long-range anti-correlations. The results suggest that the fluctuation exponent provides complementary information to the fractal dimension.
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