This paper explores the possibility of using vector fields to design and implement reactive schedules for safe cooperative robot patterns on graphs. The word "safe" means that obstacles - designated illegal portions of the configuration space - are avoided. The word "cooperative" connotes situations wherein physically distributed agents are collectively responsible for executing the schedule. The word "pattern" refers to tasks that cannot be encoded simply in terms of a point goal in the configuration space. The word "reactive" will be interpreted as requiring that the desired pattern be asymptotically stable: conditions close but slightly removed from those desired remain close and converge toward the desired pattern. We consider Automated Guided Vehicles (AGV's) operating upon a predefined network of pathways, contrasting the simple cases of locally Euclidean configuration spaces with the more topologically intricate non-manifold cases. The focus of the present inquiry is the achievement of safe cooperative patterns by means of a succession of edge point fields combined with a circulating field to regularize collisions at non-manifold vertices. For more information: Kod*Lab