An evolution strategy is proposed to construct neutral graphs. The proposed method is applied to the construction of the neutral graph of Boolean regulatory networks that share the same state sequences of the cell cycle of the fission yeast. The regulatory networks in the neutral graph are analyzed, identifying characteristics of the networks which belong to the connected component of the fission yeast cell cycle network and the regulatory networks that are not in the connected component. Results show not only topological differences, but also differences in the state space between networks in the connected component and the rest of the networks in the neutral graph. It was found that regulatory networks in the fission yeast cell cycle network connected component can be mutated (change in their interaction matrices) no more than three times, if more mutations occur, then the networks leave the connected component. Comparisons with a standard genetic algorithm shows the effectiveness of the proposed evolution strategy.