Use Tutte embedding to lay out vertices of a graph.
Details & Suboptions
The Tutte embedding is a graph-drawing technique to position vertices of a graph so that the outer face is a convex polygon and each interior vertex is at the mean of the positions of its adjacent vertices.
The Tutte embedding is typically used to lay out planar graphs.
Place vertices without crossing edges and minimize the sum of distances to neighbors:
"TutteEmbedding" works for 3-connected planar graphs only: