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It is well known that the selection of fixation probability is the fundamental problem for the evolutionary dynamics in structured populations. This paper aims to introduce a general approach for investigating the evolutionary dynamics in a class of structured populations. It includes the evolutionary game dynamics and constant selection dynamics with different asynchronous updating rules, such as ‘birth-death’, ‘voter model’, ‘death-birth’, and ‘imitation’. It should be pointed out that the proposed method provides an effective way to resolve the evolutionary dynamics on general graphs. In particular, it introduces a useful calculating tool to analyze various evolutionary dynamics on small order graphs.