In this second part of the paper we exploit the framework of Partial difference Equations (PdEs) over graphs for analyzing the behavior of multi-agent systems equipped with potential field based control schemes. We consider agent dynamics affected by errors and model the collective dynamics through nonlinear PdEs. Hinging on the properties of the Laplacian operator on graph, discussed in Part I, we prove alignment and collision avoidance both in leaderless and leader-follower models.