Ways to map a directed acyclic graph to a grid / matrix

Question

I have a DAG with many thousands of vertices and edges.

I am looking for algorithms that can position vertices on grid points in such a way that it is the friendliest person / aesthetics. My guess is that the most beautiful layout will look like a layout with a minimal sum of edge lengths.

Can you point me to efficient algorithms for such a minimal amount of edge length layouts or to other algorithms that could help me solve this problem?

Here is part of the way out of a very naive algorithm:

Answer 1

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