  We investigate different mean-field-like approximations for stochastic
dynamics on graphs, within the framework of a cluster-variational approach. In
analogy with its equilibrium counterpart, this approach allows one to give a
unified view of various (previously known) approximation schemes, and suggests
quite a systematic way to improve the level of accuracy. We compare the
different approximations with Monte Carlo simulations on a reversible
(susceptible-infected-susceptible) discrete-time epidemic-spreading model on
random graphs.
