Many researchers have explored effects of complex networks structure on evolutionary dynamics of mutations in recent years. One of the most interesting problems in this field is calculation of fixation time of a mutant in a population of resident species. Analytical calculation of fixation time is not easy due to statistical and complicated nature of both network structure and evolutionary dynamics. Hence, most studies on this subject have carried on numerically or by simulation. In this thesis we use the simulation of Moran process to investigate the effect of community structure of a complex network on evolutionary dynamics. To this end, we consider a special network with two communities constructed from two complete graphs which are connected to each other by few number of edges. We study the effect of a number of important parameters in this process such as Fitness, The Number of Links Connecting Two Communities, The Ratio of Sizes of Two Communities, and Initial Position of The First Mutant. Our results show that variation of these parameters have important effects on fixation process and particularly fixation time.
