How can we characterize consensus in a network of agents?

How can we characterize consensus in a network of agents? Imagine a set of artificial agents, expert systems, or decision-makers, each beginning with their own "beliefs" about a shared situation. For example, one transport agent may believe that there is a train strike, another may believe that there is no strike, and a third may believe that if there is a strike, then buses will be overcrowded. They exchange messages over a directed network whose edges represent influence: one agent revises its beliefs after hearing from another, then a different pair communicates, and so on. If influence can eventually travel from every agent to every other agent, will the group end up agreeing?