% The node incidence matrix for the graph is
A =[ 
    1  0  0  0  0  0  0  -1 0  0  0  0;
    1  0  0  0  0  0  0  -1 0  0  0  0;
    1  0  0  0  0  0  0  -1 0  0  0  0;
    0  0  1  0  0  0  0  -1 0  0  0  0;
    0  1  0  0  0  0  0  0  -1 0  0  0;
    0  1  0  0  0  0  0  0  -1 0  0  0;
    0  1  0  0  0  0  0  0  -1 0  0  0;
    0  0  0  0  0  0  1  0  -1 0  0  0;
    0  0  1  0  0  0  0  0  0  -1 0  0;
    0  0  0  1  0  0  0  0  0  -1 0  0;
    0  0  0  1  0  0  0  0  0  -1 0  0;
    0  0  0  1  0  0  0  0  0  -1 0  0;
    0  0  0  0  1  0  0  0  0  0  -1 0;
    0  0  0  0  1  0  0  0  0  0  -1 0;
    0  0  0  0  1  0  0  0  0  0  -1 0;
    0  0  0  0  1  0  0  0  0  0  -1 0;
    0  0  0  0  0  0  1  0  0  0  -1 0;
    1  0  0  0  0  0  0  0  0  0  0  -1;
    0  0  1  0  0  0  0  0  0  0  0  -1;
    -1 1  0  0  0  0  0  0  0  0  0  0;
    -1 0  0  0  1  0  0  0  0  0  0  0;
    -1 0  0  0  1  0  0  0  0  0  0  0;
    0  -1 1  0  0  0  0  0  0  0  0  0;
    0  -1 0  1  0  0  0  0  0  0  0  0;
    0  -1 0  0  1  0  0  0  0  0  0  0;
    0  -1 0  0  0  1  0  0  0  0  0  0;
    0  0  -1 0  1  0  0  0  0  0  0  0;
    0  0  0  -1 1  0  0  0  0  0  0  0;
    0  0  0  -1 1  0  0  0  0  0  0  0;
    0  0  0  -1 1  0  0  0  0  0  0  0;
    0  0  0  -1 1  0  0  0  0  0  0  0;
    0  0  0  -1 0  1  0  0  0  0  0  0;
    0  0  0  0  -1 0  1  0  0  0  0  0;
    0  0  0  0  0  -1 1  0  0  0  0  0;
    0  0  0  0  0  -1 1  0  0  0  0  0];

% the number of variable nodes
n = 7;
% the number of links
K = size(A,1);
% total number of nodes
N = 12;
% x and y coords for the fixed nodes
xfixed = [-1 0.8 -1 1 0]';
yfixed = [0.8 1 -1 -1 0.6]';

% plotting the randomly placed free nodes for comparison with
% the optimal quadratic placement (which will look much nicer!)
rand('seed',0)
xrand = 2*rand(n,1) - 1;
yrand = 2*rand(n,1) - 1;
view_layout(xrand,yrand,xfixed,yfixed,A);
title('Random placement of the free nodes')