  We study the dynamics of bond-disordered Ising spin systems on random graphs
with finite connectivity, using generating functional analysis. Rather than
disorder-averaged correlation and response functions (as for fully connected
systems), the dynamic order parameter is here a measure which represents the
disorder averaged single-spin path probabilities, given external perturbation
field paths. In the limit of completely asymmetric graphs our macroscopic laws
close already in terms of the single-spin path probabilities at zero external
field. For the general case of arbitrary graph symmetry we calculate the first
few time steps of the dynamics exactly, and we work out (numerical and
analytical) procedures for constructing approximate stationary solutions of our
equations. Simulation results support our theoretical predictions.
