For an asymptotically locally Euclidean (ALE) or asymptotically locally flat (ALF) gravitational instanton (M,g) with toric symmetry, we express the signature of (M,g) directly in terms of its rod structure. Applying Hitchin?Thorpe-type inequalities for Ricci-flat ALE/ALF manifolds, we formulate necessary conditions that the rod structures of toric ALE/ALF instantons must satisfy, as a step toward a classification of such spaces. Finally, we apply these results to the study of rod structures with three turning points.