Phase Transition on The Degree Sequence of a Mixed Random Graph Process

Abstract: This paper focuses on the problem of the degree sequence for a mixed random graph process which continuously combines the classical model and the BA model. Note that the number of step added edges for the mixed model is random and unbounded. By developing a comparing argument, phase transition on the degree distributions of the mixed model is revealed: while the pure classical model possesses a exponential degree sequence, the pure BA model and the mixed model possess power law degree sequences. We point out that the intermediate mixed model can be looked as a BA model with sublinear preferential attachment.