Random Matrix

  • Thread starter gradnu
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  • #1
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Does anybody know how to generate a random matrix with entries 0 and 1 only(binary matrix). Numbers of 1 and 0 are fixed every time matrix is generated.
Possibly a program in 'C'.

Thanks
 

Answers and Replies

  • #2
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Numbers are not truly random so perhaps you would like to look at random number generators. You could take your seed and square it, then take out the bits. and the square is your new seed. Or think of another mathematical formula for generating random numbers.


http://www.cprogramming.com/tutorial/random.html
The number returned by function rand is dependent on the initial value, called a seed that remains the same for each run of a program. This means that the sequence of random numbers that is generated by the program will be exactly the same on each run of the program.

You can change the seed to be the same for the matricies you wish to have the same 1/0.
 
  • #3
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is the size of the matrix random as well?
 
  • #4
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No, size of matrix is finite.
Basically the problem is to generate random networks with fixed number of nodes and fixed number of links. Network is being represented by a binary matrix where the entry '1' means that a link exists between the corresponding row and column and '0' means the link does not exist.
I have to make sure that in generating new network(or matrix) the network should remain connected. It shouldn't break into two or more smaller networks.
I haven't done graph theory so if somebody can help me with some kind of algorithm, it would be great.

Thanks,
 
  • #5
D H
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Are you generating a incidence matrix (matrix is indexed by nodes and vertices; element ij is one if node i is an endpoint of vertex j) or an adjacency matrix (element ij is one if some vertex connects node i to node j)? A network is a directed graph, so the adjacency matrix is asymmetric.

Determining whether a random NxN unitary matrix with M ones represents a digraph is the NP-complete problem called the clique problem.
 
  • #6
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I want to generate random adjacency matrices where element ij is 1 if an edge connects node i to node j. Yes it is asymmetric.
 
  • #7
robphy
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I want to generate random adjacency matrices where element ij is 1 if an edge connects node i to node j. Yes it is asymmetric.

..and you wish to do so with a fixed number of "1"s?

This might not be the most efficient:

initialize A=0

For k ones,
do this k times
{
select randomly i from 1 to n, and j from 1 to n
if A[i,j]=1, go back and get another pair (without changing k)
else set A[i,j]=1
}

If necessary, discard proposed links to oneself (i.e. reject the pair if i=j).
 
Last edited:
  • #8
D H
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Nodes in a network can link to themselves. For example, in finite state machine, it is often best to explicitly represent the time steps during which the machine remains in one state as a transition from that state to that same state.

One problem with this approach is that it most likely will not generate a "network". You could wrap this approach in an outer loop that tests whether the adjacency network represents a single graph. If it doesn't, try again. Determining whether this is the case might take a lot of CPU time (its NP-complete).
 

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