MATLAB plot the solution for the Traveling Salesman Problem

I have a few points in space:

A  0 0
B  0 1
C  0 2
D  0 4
E  1 2
F  1 3
G  2 0
H  2 4
I  3 4
J  4 4
K  5 0
L  6 1
M  7 2
N  7 4
O  4 2
P  8 3
Q  8 4 ;

I also have a solution for the Traveling Salesman Problem, essentially the edges which have to be connected.

A B   1
A G   1
B C   1
C E   1
D F   1
D H   1
E F   1
G O   1
H I   1
I J   1
J N   1
K L   1
K O   1
L M   1
M P   1
N Q   1
P Q   1

I could plot the nodes but I am not sure how to specify the edges.

Use the MATLOG toolbox from Dr. Michael Kay (NC State). Free download from link (backup link).

Take a look at the pplot() documentation (link here). Specifically you can plot given the Arc List, denoted IJ in the documentation (see code below).

  % Examples:
  XY = [2 2; 3 1; 4 3; 1 4];                  % Points
  pplot(XY,'r.')
  pplot(XY,num2cell(1:4))
 
  IJ = [1 2; 1 3; 1 4];                       % Arc List
  h1 = pplot(IJ,XY,'g-');
  IJlab = {'(1,2)','(1,3)','(1,4)'};
  h2 = pplot(IJ,IJlab,XY);
  delete([h1; h2])
 
  loc = {[1 4 3 2 1]};                        % Loc Seq Vector
  h3 = pplot(loc,XY,'g-');
  loclab = {'(1,4)','(4,3)','(3,2)','(2,1)'};
  h4 = pplot(loc,loclab,XY);
  set(h3,'color','b')

This was able to quickly produce your desired plot.

Update Example using tspnneighbor() and tsp2opt() from the MATLOG function list & documentation.

This approach uses a location vector which is just the node indices in sequence, e.g. loc = [3 5 6 1 2 4 3].

% Add MATLOG directory to path
path(path,'C:\Users\username\mypathtoMATLOG')

% DATA
XY_NCcity = uscity('XY',strcmp('NC',uscity('ST'))); % Get NC city [lon, lat] coordinates
C = dists(XY_NCcity,XY_NCcity,'mi');  % Get distance matrix

% ANIMATION
% Closest Unvisited City Algorithm (Nearest Neighbor)
makemap(XY_NCcity)
h = pplot(XY_NCcity,'r.')
[loc,TC,bestvtx] = tspnneighbor(C,527,h)  % Start CUCA from node 527 (Raleigh)

Below is the output using cities in North Carolina. Further examination of the tspnneighbor( ) function shows it uses MATLOG's pplot function.

For completeness, there is also a two-opt improvement feature, tsp2opt(), which can improve the solution.

% OPTIONAL: ANIMATED TWO-OPT IMPROVEMENT
% Demonstrates what a "more optimal" tour would look like
% Final result is not guaranteed to be optimal
[loc,TC] = tsp2opt(loc,C,[],[],[],h); % Two-opt heuristic improvement