We first introduce a useful result in probability theory: if the random variable X i is distributed geometrically with parameter p i for i = 1, · · ·, n and they are independent, then ∧ i=1,· · ·,n X i is distributed geometrically with parameter 1 − According to the characteristic of the DSI model, the time cost that an infected node w spends in infecting its uninfected neighbor v is distributed geometrically with parameter ip(w, v).