By using moving frames and directred digraphs, we study invariant (1,2)-symplectic structures on complex Rag manifolds. Let F be a Rag manifold with height k - 1. We show that there is a k-dimensional family of invariant (1,2)-symplectic metrics of any parabolic structure on F. We also prove any invariant almost complex structure J on F with height 4 admits an invariant (1,2)-symplectic metric if and only ii J is parabolic or integrable.522271282