Following the prescription of Ref. \cite{PST} in which perfect state transference (PST) of a qubit over distance regular spin networks was discussed, in this paper PST of an arbitrary $d$-level quantum state (qudit) over antipodes of more general networks called pseudo distance-regular networks, is investigated. In fact, the spectral analysis techniques used in the previous work \cite{PST}, and algebraic structures of pseudo distance-regular graphs are employed to give an explicit formula for suitable coupling constants in the Hamiltonians so that the state of a particular qudit initially encoded on one site will evolve freely to the opposite site without any dynamical control, i.e., we show that how to derive the parameters of the system so that PST can be achieved. Keywords:Perfect state transfer, $d$-level quantum state, Stratification, Pseudo-distance-regular network PACs Index: 01.55.+b, 02.10.Yn

28 pages, 5 figures