The exponential degree distribution in complex networks: Non-equilibrium network theory, numerical simulation and empirical data |
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Authors: | Weibing Deng Wei Li Xu CaiQiuping A Wang |
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Institution: | a ISMANS, 44 Ave. Bartholdi, F-72000 Le Mans, Franceb Complexity Science Center & Institute of Particle Physics, Hua-Zhong (Central China) Normal University, Wuhan 430079, Chinac LPEC, UMR CNRS 6087, Université du Maine, F-72085 Le Mans, Franced Max-Planck Institute for Mathematics in the Sciences, Inselstr. 22-26, D-04103 Leipzig, Germany |
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Abstract: | The exponential degree distribution has been found in many real world complex networks, based on which, the random growing process has been introduced to analyze the formation principle of such kinds of networks. Inspired from the non-equilibrium network theory, we construct the network according to two mechanisms: growing and adjacent random attachment. By using the Kolmogorov-Smirnov Test (KST), for the same number of nodes and edges, we find the simulation results are remarkably consistent with the predictions of the non-equilibrium network theory, and also surprisingly match the empirical databases, such as the Worldwide Marine Transportation Network (WMTN), the Email Network of University at Rovira i Virgili (ENURV) in Spain and the North American Power Grid Network (NAPGN). Our work may shed light on interpreting the exponential degree distribution and the evolution mechanism of the complex networks. |
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Keywords: | Exponential degree distribution Non-equilibrium network Evolution mechanism Kolmogorov-Smirnov Test |
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