The BA model with finite-precision preferential attachment

Preferential attachment is an indispensable ingredient of the BA model and its variants. In this paper, we modify the BA model by considering the effect of finite-precision preferential attachment, which exists in many real networks. Finite-precision preferential attachment refers to existing nodes with preferential probability Π varying within a certain interval, which is determined by the value of a given precision, being considered to have an equal chance of capturing a new link. The new model reveals a transition from exponential scaling to a power-law distribution along with the increase of the precision. Epidemic dynamics and immunization on the new network are investigated and it is found that the finite-precision effect should be considered in tasks such as infection rate prediction or immunization policy making.