On the cycles of Boolean networks

Using semi-tensor product, the Boolean network is converted into its algebraic form as a standard discrete-time linear system. From the rank and 1-eigenvector of structure matrix, we obtain the cycle structure of the Boolean network, such as the cycles and the number of the cycles with different length. In this paper, we just use the rank and 1-eigenvector of structure matrix to obtain the results, while in literature the different powers of structure matrix are used.