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+ ... + Cn*[(xn-x0)2+(yn-y0)2]1/2
where CN is the edge width between nodes N and 0, and xN and yN are points connected to x0, y0
with partial derivatives:
df/dx0=
CN*2*(x0-x1)/2*[(x1-x0)2+(y1-y0)2]2 + ... = 0
and
df/dy0= ...
which we can solve for numerically.