  We study two agent based models of opinion formation - one stochastic in
nature and one deterministic. Both models are defined in terms of an underlying
graph; we study how the structure of the graph affects the long time behavior
of the models in all possible cases of graph topology. We are especially
interested in the emergence of a consensus among the agents and provide a
condition on the graph that is necessary and sufficient for convergence to a
consensus in both models. This investigation reveals several contrasts between
the models - notably the convergence rates - which are explored through
analytical arguments and several numerical experiments.
