Mutation testing is a method widely used to evaluate the effectiveness of the test suite in hardware and software tests or to design new software tests. In mutation testing, the original model is systematically mutated using certain error assumptions. Mutation testing is based on well-defined mutation operators that imitate typical programming errors or which form highly successful test suites. The success of test suites is determined by the rate of killing mutants created through mutation operators. Because of the high number of mutants in mutation testing, the calculation cost increases in the testing of finite state machines (FSM). Under the assumption that each mutant is of equal value, random selection can be a practical method of mutant reduction. However, in this study, it was assumed that each mutant did not have an equal value. Starting from this point of view, a new mutant reduction method was proposed by using the centrality criteria in social network analysis. It was assumed that the central regions selected within this frame were the regions from where test cases pass the most. To evaluate the proposed method, besides the feature of detecting all failures related to the model, the widely-used W method was chosen. Random and proposed mutant reduction methods were compared with respect to their success by using test suites. As a result of the evaluations, it was discovered that mutants selected via the proposed reduction technique revealed a higher performance. Furthermore, it was observed that the proposed method reduced the cost of mutation testing.