Is there a way to project a graph onto a subspace? If so, is this a useful thing to do? Well starting out with a 6 node undirected graph:

Choose a orthogonal projection matrix \(P\) for the \(A, B, C\) "plane?".

Do the multiplication to get

The result is a directed graph where \(D, E, F\) lose their outgoing edges. Transposing the graph flips the arrows. That's more in line with the idea of projection.