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Volume 6, Number 4, 2016, Pages 1105-1113                                                                DOI:10.11948/2016072
Degree Sequences Beyond Power Laws in Complex Networks
Zhanying Zhang,Wenjun Xiao,Guanrong Chen
Keywords:Network, degree variable sequence, power-law distribution, general distribution.
      Many complex networks possess vertex-degree distributions in a power-law form of $ck^{-\gamma}$, where $k$ is the degree variable and $c$ and $\gamma$ are constants. To better understand the mechanism of power-law formation in real-world networks, it is effective to analyze their degree variable sequences. We had shown before that, for a scale-free network of size $N$ ,if its vertex-degree sequence is $k_11$ , then the length $l$ of the vertex-degree sequence is of order $logN$ . In the present paper, we further study complex networks with more general distributions and prove that the same conclusion holds even for non-network type of complex systems. In addition, we support the conclusion by verifying many real-world network and system examples. We finally discuss some potential applications of the new finding in various fields of science, technology and society.
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