title: Origin of Gibrat law in Internet: asymmetric distribution of the correlation.
abstract: Although Gibrat's law and its generalized versions have been widely used, the organizing principle behind its phenomenological theory has been poorly studied for network-structured systems. More important, its fluctuation behavior, which contradicts the prediction of the preferential attachment (PA), indicates a nontrivial mechanism that goes beyond our present knowledge based on the traditional mean-field approach. Here, we take advantage of the rich data of the Internet and aim to identify the origin of Gibrat's law by studying the empirical fluctuation behavior. We show how the correlation between the fluctuations of the node degree increment affects the dynamics of the network. Specifically, if the distribution of the correlation is symmetric, the network evolves as the classical PA, while if such symmetry breaks, the fluctuation becomes macroscopically positively correlated and contributes to the emergence of Gibrat's law. These results indicate a local collective increase in the actual network evolution, which provides a new paradigm and understanding of the related microcosmic dynamics.
authors.affiliation: Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China.
authors.forename: Jiang-Hai
authors.initials: JH
authors.lastname: Qian
authors.affiliation: School of Information Science and Technology, East China Normal University, Shanghai 200241, China.
authors.forename: Qu
authors.initials: Q
authors.lastname: Chen
authors.affiliation: School of Information Science and Technology, East China Normal University, Shanghai 200241, China.
authors.forename: Ding-Ding
authors.initials: DD
authors.lastname: Han
authors.affiliation: Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China and School of Physical Science and Technology, Shanghai Tech University, Shanghai 200031, China.
authors.forename: Yu-Gang
authors.initials: YG
authors.lastname: Ma
authors.affiliation: Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China and School of Physical Science and Technology, Shanghai Tech University, Shanghai 200031, China.
authors.forename: Wen-Qing
authors.initials: WQ
authors.lastname: Shen
mesh_terms: D003198:Computer Simulation; D016247:Information Storage and Retrieval / Q000706:statistics & numerical data*; D020407:Internet / Q000706:statistics & numerical data*; D015233:Models, Statistical; D013223:Statistics as Topic