creating matrix from data-set

Question

I have a network with edges and points. The FID shows the ID number of each edge that is created by Start_Point and End_Point. For example edge 3 is between the two points of 2 and 3 in the network.

FID     Start_Point End_Point
1       1           2
2       1           4
3       2           3
4       2           4

I want to create a 4-by-4 matrix of these points. if there is an edge between 2 points the value is 1 else is inf:

[inf, 1,   inf, 1;
 1,   inf, 1,   1;
 inf, 1,   inf, inf;
 1,   1,   inf, inf]

How can I create such a matrix in MATLAB?

Answer 1

You can convert it to a sparse matrix and then use full command to obtain adjacency matrix.

edges= [1 2;
    3 4;
    3 1
    2 3];
n=size(edges,1);
% create sparse matrix with given edges and their reverse direction
A = sparse([edges(:,1); edges(:,2)],[edges(:,2); edges(:,1)],[ones(n,1); ones(n,1)]);
% create adjacency matrix
B=full(A);
% set zeros to inf
B(B==0)=inf;

and this is the result :

A =

   (2,1)        1
   (3,1)        1
   (1,2)        1
   (3,2)        1
   (1,3)        1
   (2,3)        1
   (4,3)        1
   (3,4)        1

>> B

B =

   Inf     1     1   Inf
     1   Inf     1   Inf
     1     1   Inf     1
   Inf   Inf     1   Inf

Edit : the sparse command create a sparse matrix with addressing values of its elements. One prototype for this command is as follow :

A=sparse(rows,cols,values);

for example A=sparse([1;2],[1,3],[10,5]) is a matrix which A(1,1)=10 and A(2,3)=5 and other elements are zero:

A=sparse([1;2],[1,3],[10,5]);
>> full(A)

ans =

    10     0     0
     0     0     5

In your case you have to add two directions to sparse matrix (symmetric) and all values are one. So you need to construct sparse matrix as :

 A = sparse([edges(:,1); edges(:,2)],[edges(:,2); edges(:,1)],[ones(n,1); ones(n,1)]);

full command convert a sparse matrix to a dense one.

Answer 2

So you basically want to create an adjacency matrix from an adjacency list of edges? The number of your edges (i.e. your FID column) is irrelevant so I'm assuming your input data is of the form

edges = [1   2
         1   4
         2   3
         2   4]

Now the first column of edges is the rows of your adjacency matrix and the second is the columns (or vice versa, it doesn't matter since your matrix is symmetrical)

The simplest solution is to use linear index which you would get via the sub2ind function:

adj = inf(size(edges,2));
idx = sub2ind(size(adj),edges(:,1), edges(:,2))
adj(idx) = 1;

I suspect your edges matrix will already be symmetrical but if it's not then just use

edges_sym = [edges; fliplr(edges)]

instead of edges

Answer 3

You can use accumarray:

edges1 = accumarray([startpoint endpoint]),1);
edges2 = edges1.'; % transpose your matrix, to obtain both edges
edges = edges1+edges2;
edges(edges==0)=inf;

accumarray gathers all points with common indices, pastes the value 1 on those indices. edges1 is the transpose of edges2, thus transpose, then add the two together. Find all indices on which the matrix is 0, then fill those values with inf.

Alternative:

edges= [1 2;
    3 4;
    3 1
    2 3];
matrix = accumarray([edges;fliplr(edges)],1,[],[],inf);

fliplr flips your matrix left to right, to get all the desired combinations of indices. Then use accumarray to set a 1 on all locations specified by edges and put inf at the other locations.

If you are sure your matrix is symmetric, don't use fliplr, if you sure your matrix is non-symmetric, use fliplr and if you are not sure use this:

matrix = accumarray([edges;fliplr(edges)],1,[],@mean,inf);

where the @mean makes sure to set double entries to 1 anyway. For weighted edges do the following, where weights is an Nx1 array containing the weights and N is the number of edges.

matrix = accumarray([edges;fliplr(edges)],weights,[],@mean,inf);