Phase transition on the degree sequence of a random graph process with vertex copying and deletion

This paper focuses on the degree sequence of a random graph process with copying and vertex deletion. A phase transition is revealed as the following: when copying strictly dominates deletion, the model possesses a power law degree sequence; and when deletion strictly dominates copying, it possesses an exponential   one; otherwise, the model possesses an intermediate degree distribution which decays as e−ck. Note that, due to copying, the edge number of the model may grow super-linearly and the model may exhibit a power law with any exponent greater than 1.