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I know for the fact that square binary matrix can be converted to a graph. For example using gplot in matlab matrix below can be converted to the graph

0 1 1 
1 0 0
0 1 0

can be represented by a graph 

A->B, A->C, B->A,C->B

But I wonder if there is a way to convert a rectangular matrix like

0 1
1 0
0 1

to a graph someway in matlab or any other language?

Also my rows and columns are different variables.

discipulus
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    And what does that rectangular matrix mean exactly? – Eitan T Dec 11 '12 at 09:53
  • Rectangular matrix means number of rows and columns are different. The problem with this is that it will not exactly be adjacency matrix for a graph. – discipulus Dec 11 '12 at 10:00
  • I didn't ask about the word "rectangular". I asked about what it represents. What meaning is there to an adjacency matrix when the number of rows is not equal to the number of columns? – Eitan T Dec 11 '12 at 10:05
  • As I told initially they represent different variables ... For example rows are the customers and columns are the items they bought, popularly known as market basket data. This traditionally will not be a graph but I guess presence of some graphical structures in the data. – discipulus Dec 11 '12 at 10:25
  • Then please provide an example of the graphical representation you want to obtain... – Eitan T Dec 11 '12 at 13:11

2 Answers2

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If you're indeed interested in a Bipartite graph, like @Ante has suggested, you can make clever use of gplot here as well:

  1. First create a square adjacency matrix by padding your rectangular matrix with zero-columns:

    A = [0 1; 1 0; 0 1];
Asq = eye(sum(size(A)));
Asq(1:size(A, 1), end - size(A, 2) + 1:end) = A;

  2. Let's decide that the rows vertices will be on the left side and the column vertices will be on the right side. Now create a matrix of coordinates for the vertices:

    xy1 = [ones(size(A, 1), 1), (1:size(A, 1))'];      % # Row vertices
xy2 = [2 * ones(size(A, 2), 1), (1:size(A, 2))'];  % # Column vertices

  3. Plot the graph:

    gplot(Asq, [xy1; xy2], '*-')
axis([0, 3, 0, size(A, 1) + 1])

This is what you should get for your example: enter image description here

Eitan T
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In case of different nodes for rows and columns, it is adjacency matrix of Bipartite graph.

Ante
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