How to get connected component from adjacency matrix

The adjacency matrix is already known.

what I want to do is showed in the picture below.

I don't care about the order of the vertex.

Answer 1

[Guillaume]

A lot of graph functions have been added in R2015b. In particular, you have conncomp which gives you exactly what you want:

adjacencyMatrix =[0 1 1 0 1 0 1 0 1 0
    1 0 1 0 1 0 1 0 1 0
    1 1 0 0 1 0 1 0 1 0
    0 0 0 0 0 0 0 1 0 0
    1 1 1 0 0 0 1 0 1 0
    0 0 0 0 0 0 0 0 0 1
    1 1 1 0 1 0 0 0 1 0
    0 0 0 1 0 0 0 0 0 1
    1 1 1 0 1 0 1 0 0 0
    0 0 0 0 0 1 0 1 0 0]
G = graph(adjacencyMatrix);
plot(G);  %view the graph
bins = conncomp(G);
binnodes = accumarray(bins', 1:numel(bins), [], @(v) {sort(v')});
fprintf('number of Regions = %d\n\n', numel(binnodes));
for binidx = 1:numel(binnodes)
    fprintf('All these nodes are connected:%s\n', sprintf(' %d', binnodes{binidx}));
end
fprintf('\n');

[lingfeng zhou]

It's great and that's exactly what I want. I have never contact with this function before.Thank you so much.

[ali ganjbakhsh]

so tnx

Answer 2

[Image Analyst]

Use bwlabel() and regionprops:

[labeledMatrix, numberOfRegions] = bwlabel(A);
props = regionprops(labeledMatrix, 'PixelList');

labeledMatrix gives an ID number to each connected region. props has all the information on all the elements in each connected region. You can get indexes (rows and columns), values, areas, etc. depending on what you ask regionprops() for.

[lingfeng zhou]

Thanks for your answer!

But maybe I didn't introduce my question very clear.

What I have is "adjacency matrix", which means the relation between vertex and edge. And maybe bwlabel() is more suitable for a Binary Image problem rather than my problem.

Here is another example to introduce my question.

There are 6 vertex and 3 identity connected regions.

If I use bwlabel(), the vertex "1" maybe ignored.

[Image Analyst]

Yeah, I got it. I'm not sure you understand so I'll do the full blown demo with both of your cases so that you can see it tells you all the nodes that are connected:

% Example 1
adjacencyMatrix = false(6);
adjacencyMatrix(2, 3:4) = true;
adjacencyMatrix(3:4, 2) = true;
adjacencyMatrix(5, 6) = true;
adjacencyMatrix(6, 5) = true
[labeledMatrix, numberOfRegions] = bwlabel(adjacencyMatrix)
props = regionprops(labeledMatrix, 'PixelList');
for regions = 1 : numberOfRegions
  fprintf('All these nodes are connected: ');
  fprintf('%d ', unique(props(regions).PixelList));
  fprintf('\n');
end

% Example 2
adjacencyMatrix = false(6);
adjacencyMatrix(1, 3) = true;
adjacencyMatrix(2, 3:4) = true;
adjacencyMatrix(3, [1,2,4]) = true;
adjacencyMatrix(4, 2:3) = true;
adjacencyMatrix(5, 6) = true;
adjacencyMatrix(6, 5) = true
[labeledMatrix, numberOfRegions] = bwlabel(adjacencyMatrix)
props = regionprops(labeledMatrix, 'PixelList');
for regions = 1 : numberOfRegions
  fprintf('All these nodes are connected: ');
  fprintf('%d ', unique(props(regions).PixelList));
  fprintf('\n');
end

In the command window you'll see this for example 1:

adjacencyMatrix =
     0     0     0     0     0     0
     0     0     1     1     0     0
     0     1     0     0     0     0
     0     1     0     0     0     0
     0     0     0     0     0     1
     0     0     0     0     1     0
labeledMatrix =
     0     0     0     0     0     0
     0     0     1     1     0     0
     0     1     0     0     0     0
     0     1     0     0     0     0
     0     0     0     0     0     2
     0     0     0     0     2     0
numberOfRegions =
     2
All these nodes are connected: 2 3 4 
All these nodes are connected: 5 6

and this for example 2:

adjacencyMatrix =
     0     0     1     0     0     0
     0     0     1     1     0     0
     1     1     0     1     0     0
     0     1     1     0     0     0
     0     0     0     0     0     1
     0     0     0     0     1     0
labeledMatrix =
     0     0     1     0     0     0
     0     0     1     1     0     0
     1     1     0     1     0     0
     0     1     1     0     0     0
     0     0     0     0     0     2
     0     0     0     0     2     0
numberOfRegions =
     2
All these nodes are connected: 1 2 3 4 
All these nodes are connected: 5 6

Isn't that what you want to know? Which nodes are all part of the same group? I thought it was. Correct me if I'm wrong.

By the way, bwlabel does not ignore single isolated nodes, but you can remove those in advance if you want with the bwmorph()'s "Clean" option.

[lingfeng zhou]

Well, thanks for your patience. I know the meaning of your method now, but there seems to be a little different with what I want to know.

For example, the answer I want is:

numberOfRegions =

     3
    All these nodes are connected: 1
    All these nodes are connected: 2 3 4
    All these nodes are connected: 5 6

Here,I want to give a more complex example,

% example 01
adjacencyMatrix =[0 1 0 0 0 0 0 0 0 0
    1 0 1 0 0 0 0 0 0 0
    0 1 0 1 0 0 0 0 0 0
    0 0 1 0 0 0 0 0 0 0
    0 0 0 0 0 1 1 1 1 1
    0 0 0 0 1 0 1 1 1 1
    0 0 0 0 1 1 0 1 1 1
    0 0 0 0 1 1 1 0 1 1
    0 0 0 0 1 1 1 1 0 1
    0 0 0 0 1 1 1 1 1 0]

[labeledMatrix, numberOfRegions] = bwlabel(adjacencyMatrix)
props = regionprops(labeledMatrix, 'PixelList');
for regions = 1 : numberOfRegions
  fprintf('All these nodes are connected: ');
  fprintf('%d ', unique(props(regions).PixelList));
  fprintf('\n');
end

matlab answer is:

adjacencyMatrix =

       0     1     0     0     0     0     0     0     0     0
       1     0     1     0     0     0     0     0     0     0
       0     1     0     1     0     0     0     0     0     0
       0     0     1     0     0     0     0     0     0     0
       0     0     0     0     0     1     1     1     1     1
       0     0     0     0     1     0     1     1     1     1
       0     0     0     0     1     1     0     1     1     1
       0     0     0     0     1     1     1     0     1     1
       0     0     0     0     1     1     1     1     0     1
       0     0     0     0     1     1     1     1     1     0

labeledMatrix =

       0     1     0     0     0     0     0     0     0     0
       1     0     1     0     0     0     0     0     0     0
       0     1     0     1     0     0     0     0     0     0
       0     0     1     0     0     0     0     0     0     0
       0     0     0     0     0     2     2     2     2     2
       0     0     0     0     2     0     2     2     2     2
       0     0     0     0     2     2     0     2     2     2
       0     0     0     0     2     2     2     0     2     2
       0     0     0     0     2     2     2     2     0     2
       0     0     0     0     2     2     2     2     2     0

numberOfRegions =

       2

All these nodes are connected: 1 2 3 4 
All these nodes are connected: 5 6 7 8 9 10

Another example

% Example 2
  adjacencyMatrix =[0 1 1 0 1 0 1 0 1 0
      1 0 1 0 1 0 1 0 1 0
      1 1 0 0 1 0 1 0 1 0
      0 0 0 0 0 0 0 1 0 0
      1 1 1 0 0 0 1 0 1 0
      0 0 0 0 0 0 0 0 0 1
      1 1 1 0 1 0 0 0 1 0
      0 0 0 1 0 0 0 0 0 1
      1 1 1 0 1 0 1 0 0 0
      0 0 0 0 0 1 0 1 0 0]

    [labeledMatrix, numberOfRegions] = bwlabel(adjacencyMatrix)
    props = regionprops(labeledMatrix, 'PixelList');
    for regions = 1 : numberOfRegions
      fprintf('All these nodes are connected: ');
      fprintf('%d ', unique(props(regions).PixelList));
      fprintf('\n');
    end

matlab answer is:

adjacencyMatrix =

       0     1     1     0     1     0     1     0     1     0
       1     0     1     0     1     0     1     0     1     0
       1     1     0     0     1     0     1     0     1     0
       0     0     0     0     0     0     0     1     0     0
       1     1     1     0     0     0     1     0     1     0
       0     0     0     0     0     0     0     0     0     1
       1     1     1     0     1     0     0     0     1     0
       0     0     0     1     0     0     0     0     0     1
       1     1     1     0     1     0     1     0     0     0
       0     0     0     0     0     1     0     1     0     0

labeledMatrix =

       0     1     1     0     4     0     5     0     5     0
       1     0     1     0     4     0     5     0     5     0
       1     1     0     0     4     0     5     0     5     0
       0     0     0     0     0     0     0     5     0     0
       2     2     2     0     0     0     5     0     5     0
       0     0     0     0     0     0     0     0     0     5
       3     3     3     0     3     0     0     0     5     0
       0     0     0     3     0     0     0     0     0     5
       3     3     3     0     3     0     3     0     0     0
       0     0     0     0     0     3     0     3     0     0

numberOfRegions =

       5

All these nodes are connected: 1 2 3 
All these nodes are connected: 1 2 3 5 
All these nodes are connected: 1 2 3 4 5 6 7 8 9 10 
All these nodes are connected: 1 2 3 5 
All these nodes are connected: 1 2 3 4 5 6 7 8 9 10

From the above two examples we can find that the answer will change if we only change the node order.

[lingfeng zhou]

And the answer I want is :

numberOfRegions = 2
All these nodes are connected: 1 2 3 5 7 9
All these nodes are connected: 4 6 8 10

[Image Analyst]

You can't get that with regionprops. You'll have to look at graph/node/network functions. I'm not familiar with those.

[lingfeng zhou]

Thank you anyway!

[Image Analyst]

Unaccept my Answer and see if Guillaume's gives you the answer and if it does, accept his answer to give him credit.