Organizing an adjacency matrix to build a field diagram?

Question

Programming

Good afternoon. I think about such a task. Graphically I'm trying to depict a subfield diagram. Naturally, connecting the points along the adjacency matrix, I will get something like this:

Now we need to optimize the adjacency matrix so that it does not connect, for example, 12 with 2, because 12 is already connected with 6, and 6 with 2.
How to optimize the adjacency matrix, someone has an algorithm in mind, I would be grateful.