How do you add unique values to each entry in a matrix via a loop?

I am trying to create matrix in a loop such that we are recording each vertex per edge on this (or of any number of verticies) square - apologies for the poorly drawn square. From here I want to record each vertex with connected edge like:

M= 1 2 5 0 0 0 0

1 2 3 5 6 0 0

.............

(6) 2 3 5 6 7 9 10

......................

12 15 12 0 0 0

where 0 represent that there are no other connections (to give an nxn matrix). I am doing this to build a connection matrix for a finite element process, so I can build global matricies.

My initial thoughts are

%npoint in this case is 4. 
nodes=zeros(npoint^2,npoint)
for i=1:npoint
    for j=1:npoint
                if i<=npoint && j<=npoint
                    nodes(i,j)=i
                    nodes(i,i+npoint-3)=i+1
                    nodes(i,i+npoint-2)=i+npoint
                end 
    end
end

but this just overwrites my entries - as you would expect.

If someone could offer any adivse on how to do this or a better approach, I would appreciate it greatly!

[Bob Thompson]

I'm a little bit confused what you're looking for here. The code you posted seems to only print values into the array for the final value of each loop. If you only want to print values for when i and j == npoint then why not just specify that that is the index, rather than looping through all of the other values?

[KieranSQ]

Thank you for your comment. So what I am trying to do is take each vertex in the square and see what it is connected to. From there I want to store the vertex index in a matrix where I can, later, pull out the values to be able to create a global matrix from a smaller local matrix. So I need to consider each vertex (1,2,.....,npoint) in this case i=1,2,3,4 and then each connection for each vertex.

If then I want to generalise to say 60 points I'd rather not need to explicitly type each value in.

Once this is created I am then hoping to use these entries to calculate a global matrix for the finite element method.

I hope that clears my question up slightly?