The evolution of certain pair state in a quantum network with isomorphic branches, governed by the Heisenberg $XY$ Hamiltonian, depends solely on the local structure, and it remains unaffected even if the global structure is altered. All graphs which enable high-fidelity vertex state transfer can be considered as isomorphic branches of a quantum network to exhibit high-fidelity pair state transfer. The results are used to unveil the existence of pair state transfer in various graphs, including paths, cycles, and others.