How to create a symmetric random matrix with zero diagonal and with entries just 0 and 1

There is the follwoing code

d = 1000000*rand(N,1); % The diagonal values
   t = triu(bsxfun(@min,d,d.').*rand(N),1); % The upper trianglar random values
   M = diag(d)+t+t.'; % Put them together in a symmetric matrix

responding to the question "How to create a symmetric random matrix?" at MathWorks. But my question is a bit different. I was wondering if someone could help about creating a random symmetric random matrix with zero diagonal and with entries just 0 and 1.

Thanks in advance.

Answer 1

[Walter Roberson]

N = 10;
temp = randi([0 1], N, N);
d = tril(temp,-1);
M1 = d + d.'

M1 = 10×10

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

M2 = xor(temp, temp.')

M2 = 10×10 logical array
   0   0   1   1   1   0   1   0   0   1
   0   0   1   0   1   0   1   0   0   0
   1   1   0   1   1   0   1   0   1   1
   1   0   1   0   0   1   1   0   0   1
   1   1   1   0   0   0   1   1   1   0
   0   0   0   1   0   0   0   1   1   0
   1   1   1   1   1   0   0   0   1   1
   0   0   0   0   1   1   0   0   1   1
   0   0   1   0   1   1   1   1   0   0
   1   0   1   1   0   0   1   1   0   0

[Mojtaba Mohareri]

Thank you very much for your answer. What is difference between M1 and M2?

[Walter Roberson]

Different algorithms ;-)

For simplicity, for M1 an N x N matrix is generated, but then only the lower triangle is taken (discarding the information from the upper triangle), and the lower triangle is then copied for symmetry.

For M2, a full N x N random matrix is constructed, and it is xor'd with its transpose. So two random values go into making each output. The algorithm is simpler and probably faster... but perhaps not quite as obvious as is used to construct M1.

[Walter Roberson]

Timing test:

N = 1000;
temp = randi([0 1], N, N);

tic
d = tril(temp,-1);
M1 = d + d.';
toc

Elapsed time is 0.013278 seconds.

tic
M2 = xor(temp, temp.');
toc

Elapsed time is 0.009142 seconds.

Yup, the xor only takes about 2/3 of the time of the other version

[Mojtaba Mohareri]

Understood completely. Thank you very much for your help and consideration.

[Mojtaba Mohareri]

I have a related question. When I generate a random matrix (with for example the following code)

 bounds = [-15,10]; 
A = rand(m,m) * range(bounds) + bounds(1)

there is no zero entry in matrix. Could please tell me how can I create a random matrix which has zero entries as well?