Origin of Gibrat law in Internet: asymmetric distribution of the correlation.

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.