Generalized preferential attachment considering aging

Preferential Attachment (PA) models the scientific citation process. In the PA model, a new paper attaches itself to the citation network based only on the popularity of the currently existing papers. This invariably leads to a network whose degree distribution satisfies the Power Law. Yet, empirical results show that paper age should also play a role in the citation process. In other words, when references are chosen for a new paper, the age of an existing paper may also affect the choice for citing. In this paper, we derive a generalized PA model that includes the effect of aging, with analytical solution. Such a model can be used to analyze the competing influence of preferential attachment and aging effect quantitatively in citation process and explain differences in various research domains by the extent of aging. It may also serve as a general model of network formation.