Abstract
We make a survey of models of citation dynamics and focus on the preferential attachment and fitness models. We show that under certain realistic conditions these models are equivalent. In order to find the microscopic foundations of the preferential attachment mechanism, we analyze theoretically and experimentally several citation networks and demonstrate that, for a broad fitness distribution, this mechanism reduces to the fitness model. The fitness model yields the long-sought explanation for the initial attractivity K0, an elusive parameter which was left unexplained within the framework of the empirical preferential attachment model. We show that the initial attractivity is determined by the width of the fitness distribution. We compare the preferential attachment and fitness models to our microscopic model of citation dynamics based on recursive search and show that our model contains both these phenomenological models.
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