We present an inventory and the enumeration of all non-isomorphic rigidity circuits on up to 10 vertices, as well as all non-isomorphic Assur graphs on up to 11 vertices. Assur graphs and Baranov trusses are closely related. We clarify the relation between Baranov trusses and (2, 3)-tight graphs on the one hand, and between Assur groups and Assur graphs on the other hand.