To calculate the optimal placement of a node:

optimize the distance equation (when n>2):

f(x₀,y₀)=C₁*[(x₁-x₀)²+(y₁-y₀)²]^1/2+C₂*[(x₂-x₀)²+(y₂-y₀)²]^1/2+ ... + C_n*[(x_n-x₀)²+(y_n-y₀)²]^1/2

where C_N is the edge width between nodes N and 0, and x_N and y_N are points connected to x₀, y₀

with partial derivatives:

df/dx0=

C_N*2*(x₀-x₁)/2*[(x₁-x₀)²+(y₁-y₀)²]² + ... = 0

and

df/dy0= ...

which we can solve for numerically.