Recently, evolutionary dynamics on structured population has attracted an increasing attention in various fields. This paper aims at investigating the fixation probability of a mutant under random drift on a class of weighted networks. In particular, we have attained the analytical solutions of fixation probability of mutants on the weighted networks with three different updating rules, including link dynamics, Moran process, and voter model. It should be especially pointed out that the above analytical solutions can be used to further understand and control the evolution processes. Numerical simulations are also given to validate the above analytical solutions.
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