create a random matrix that satisfies specific criteria (graph theory)

Hello everyone, I have a 264 x 264 undirected (binary) adjacency matrix on which I calculate the nodal degree (or the number of edges connected to each node), which results in a 264 x 1 vector indicating the "degrees", or number of edges/connections, per node. Now what I would like to do is create a series of random matrices that have the same number of nodes with connections and nodal degree as the original matrix. As it will be random, it shouldn't matter what nodes those are, just that the overall nodal degree count is maintained. For instance, if I take a count of the original 264 x 1 vector, I have 79 nodes with no edges/connections, 58 nodes with 1 edge/connection, 23 nodes with 2 edges/connections, 22 nodes with 3 edges/connections, etc. So I need to generate a matrix that satisfies these criteria. I imagine that the code might be rather extensive to achieve this in MATLAB, but I would appreciate any guidance on this issue. Thank you so very much.

Answer 1

[Matt J]

Just permute the rows and columns of the original adjacency matrix, A,

[~,is]=sort(rand(264),2);

for k=1:264
 A(k,:)=A(k,is(k,:));
end

A=A(randperm(264),:);

[Georgette Argiris]

Hi Matt, thank you very much for your quick response. I might be wrong, but it doesn't seem to solve my issue because nodal degree changes. Sorry for the crude code...I hope it's understandable:

A = randi([0 1], 264, 264);

deg1 = sort(sum(A)); %gives sorted nodal degree

A2 = A; %just to compare output for your code below

[~,is]=sort(rand(264),2);

for k=1:264

A2(k,:)=A2(k,is(k ,:));

end

A2 = A2(randperm(264),:);

deg2 = sort(sum(A2));

min(deg1 == deg2) %this should be 1 as the nodal degree vector should be %the same

[Matt J]

Here's another possibility,

p=randperm(264);

A2=A(p,p);

though I don't know if this spans the full space of possible solutions.