I'm thinking in particular of the fact that when you have a huge contraction of tensors in rimannian geometry most of the indices are irrelevant. I'm pretty sure one can replace the whole contraption with a graph together with an order on the edges coming and going into each vertex plus a decoration of vertices by tensors. Does anyone know of such a graphical language?

There's Penrose diagrams but these are much more general and not quite what i'm looking for. In particular i'm looking for a graphical language which uses the fact that there's a non-degenerate linear form to simplify the no…