  We use zero-temperature Glauber dynamics to study hysteresis in the
random-field Ising model on directed random graphs. The critical behavior of
the model depends on the connectivity $z$ of the graph rather differently from
that on undirected graphs. Directed graphs and zero-temperature dynamics are
relevant to a wide class of social phenomena including opinion dynamics. We
discuss the efficacy of increasing external influence in inducing a first-order
phase transition in opinion dynamics. The numerical results are supported by an
analytic solution of the model.
