Step 1: Think about what graphite shape does to the matrix.
In all cast irons, free graphite is soft and adds almost no strength, so the ductility of the material is really controlled by how much the surrounding iron matrix can stretch before it tears. Graphite shape decides how badly that matrix gets notched internally.
Step 2: Compare the shapes.
Sharp graphite flakes, as in gray iron, behave like tiny built-in cracks with sharp tips, so stress concentrates enormously around them and the matrix fails with almost no stretching. The irregular rosette shaped temper carbon in malleable iron is gentler than flakes but still not perfectly rounded. A sphere, however, is the one shape that has no sharp tip at all, so stresses flow smoothly around it instead of concentrating.
Step 3: Applying this to nodular iron.
In nodular (ductile) iron the graphite is deliberately spheroidized using magnesium or cerium treatment, giving it this ideal rounded shape. With almost no stress raising notches, the ferritic or pearlitic matrix can plastically deform to a large degree before fracture, giving elongations that can rival many steels.
Step 4: Conclusion.
Since nodular cast iron minimizes internal stress concentration better than gray or malleable iron, and even outperforms many high carbon steels in this regard, it is the material with the highest ductility among the choices.
\[ \boxed{\text{Nodular cast iron}} \]