If i have 10 random (x,y) coordinates in form of Z given below gives the location of nodes.How to give number labelling to these coordinates?And how to construct a (node and link i.e G(v,e) )graph with weights equal to the distance between the nodes?

z =

     9     0
     5     1
    10     4
     1     3
     0     0
     7     1
     4     4
     8     4
     0     5
     4     1

here X1=(9,0),X2=(5,1)..X10=(4,1) How to label the coordinates 1,2 3....10 And how to construct graph ie G= graph(s,t,weights) where weights is the distance between the nodes/coordinates

Answer 1

[Rollin Baker]

Hi Sneha,

You can create your graph using the "digraph" function, and determine the weights using the "pdist" function. This can achieved with the following code:

 % Define the coordinate points of the nodes
 z = [ 9, 0; 5, 1; 10, 4; 1, 3; 0, 0; 7, 1; 4, 4; 8, 4; 0, 5; 4, 1];

 % Get the x and y coordinates of the nodes
 xPoints = z(:, 1);
 yPoints = z(:, 2);

 % Define the source nodes of the edges
 s = [1 2 3 4 5 6 7 8 9];

 % Define the destination nodes of the edges
 t = [2 3 4 5 6 7 8 9 10];

 % Initialize the weights array
 weights = zeros(1, numel(s));

 % Define the weights
 for idx = 1:numel(weights)
    weights(idx) = pdist([z(idx, :); z(idx + 1, :)]);
 end

 % Create graph
 G = digraph(s,t, weights);

 % Plot the graph with edge weights
 p = plot(G, 'EdgeLabel', G.Edges.Weight);

 % Set the x-coordinates of the nodes
 p.XData = xPoints;

 % Set the y-coordinates of the nodes
 p.YData = yPoints;

Since you didn't specify the connectivity of the graph, I assumed X1 was connected to X2, X2 was connected to X3, and so on. This can be changed by altering the definitions of s and t.

The default labeling of the nodes will be the number assigned to them in the definitions for s and t, so as long as you define the edges correctly, you won't have to worry about any explicit labeling.

For more detailed documentation on using the digraph function, you can check out the link below:

https://www.mathworks.com/help/matlab/ref/graph.html

Good luck with your graph project!

-Rollin