Fluctuation behavior of the degree growth dynamics in complex networks

Abstract

The standard network theory predicts the fluctuation of the degree growth rate is interval-independent, whereas the evidence witnessed in Internet shows an inconsistent result, which raises the concern of many existing relevant studies that apply just single observation interval. To check whether such inconsistency occurs in more systems, we study empirically the degree growth fluctuations in two social networks. We find both their fluctuation exponents decrease logarithmically with the observation interval, presenting clear interval dependency that differs from those observed in Internet in the specific manner but is still consistent in the tendency. By applying a progressive shuffling procedure, we find an asynchronous response of the fluctuation exponent and deduce the decline of the exponent might be related to the development of the internal correlation. These results indicate the general existence of the interval dependency in the degree growth fluctuation and suggest its close connection with the correlation evolution, which could provide new insight to the related dynamics in complex networks.