  The fixation probability of a mutant in the evolutionary dynamics of Moran
process is calculated by the Monte-Carlo method on a few families of
clique-based graphs. It is shown that the complete suppression of fixation can
be realized with the generalized clique-wheel graph in the limit of small
wheel-clique ratio and infinite size. The family of clique-star is an
amplifier, and clique-arms graph changes from amplifier to suppressor as the
fitness of the mutant increases. We demonstrate that the overall structure of a
graph can be more important to determine the fixation probability than the
degree or the heat heterogeneity. The dependence of the fixation probability on
the position of the first mutant is discussed.
