  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 and
Barab\'{a}si-Albert graphs. We performed stochastic simulations and use
mean-field type approximations to obtain analytical formulas. We showed that
the initial placement of a mutant has a significant impact on the fixation
probability 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 results
in a decreased fixation probability and a shorter time to extinction.
