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We study the effect of the mutant's degree on the fixation probability,extinction and fixation times, in the Moran process on Erd\"{o}s-R\'{e}nyi andBarab\'{a}si-Albert graphs. We performed stochastic simulations and usemean-field type approximations to obtain analytical formulas. We showed thatthe initial placement of a mutant has a significant impact on the fixationprobability and extinction time, while it has no effect on the fixation time.In both types of graphs, an increase in the degree of a initial mutant resultsin a decreased fixation probability and a shorter time to extinction.

Effect of the degree of an initial mutant in Moran processes in structured populations