Opinion dynamics is widely used in different areas from physics to social networks. On the other hand, the complex dynamical system properties of opinion dynamics is not well understood. In opinion dynamics, every system element has an initial opinion and this opinion is updated at time t+1 by an update function depending on its neighbors opinion at time t. In a bounded confidence model, two elements interact with each other, if their opinion difference is less than a given threshold value. If the system reaches the equilibrium in a bounded confidence model, then either two neighbors have the same opinion or their opinion difference is greater than given threshold. I will talk about necessity and sufficient graph structural properties and conditions for plurality of opinion in equilibrium of bounded confidence opinion dynamics. This is a joint work with Kaan Öztürk.