Hamiltonian flows play vital roles in dynamical systems. Famous examples include the Schrodinger equation, Schrodinger bridge problem and Mean field games. In this talk, we introduce these Hamiltonian flows on finite graphs. Our approach is based on the optimal transport metric in probability simplex over finite graphs, named probability manifold. We derive these Hamiltonian flows in probability manifold. The connection between Shannon-Boltzmann entropy and Fisher information will be established in these Hamiltonian flows. Several examples are provided.