The transfer of quantum states plays an important role in quantum information processing. In fact, the transfer of a quantum state from point A to point B with unit fidelity has been the center of attention during the last decades. One of the ways to aim this goal is to transfer a quantum state in a spin chain described by designing a Hamiltonian in which amirror symmetry with respect to the network center is created. In this paper, we introduce a method based on the spectral distribution of the adjacency matrix and stratifying a spin network, with respect to an arbitrary vertex denoted by o which is called starting vertex (reference vertex), to make perfect quantum state transfer possible between antipodes in the spin network. Then we design the coupling coefficients in a way to create a mirror symmetry in the Hamiltonian with respect to the center of the network. In this method the initial state is encoded on the starting vertex and then it is received at its antipode. There is no need to consider any external control in this approach.
