Cooperation and competition are two typical interactional relationships in natural and engineering networked systems. Some interesting collective behaviors can emerge through local interactions within the networked systems. This paper focuses on the coexistence of competition and cooperation (i.e., coopetition) at the network level and, simultaneously, the collective dynamics on such coopetition networks. The coopetition network is represented by a directed signed graph. The interaction relationship between the agents on the coopetition network is described by a multi-agent system. We investigate two bipartite consensus strategies for the agents such that all the agents converge to a final state characterized by identical modulus but opposite sign. Under a weak connectivity assumption that the signed network has a spanning tree, some sufficient conditions are derived for bipartite consensus of multi-agent systems with the help of a structural balance theory. Finally, simulation results are provided to demonstrate the bipartite consensus formation.