Abstract We study opinion oscillation of the nonconsensus opinion model (NCO) on graphs, and in particular on bipartite graphs. Using intensive numerical simulations, we investigate the relationship between amplitude A (the percentage of nodes whose opinions oscillate) and ( p , q ) , which are the initial configuration fractions with opinion 1 on two sets of two bipartite graphs. Finally, for the general graph, we present several definitions and develop three propositions as regards whether an oscillation can occur or not on a certain graph.