December 4th, 2009, 12:23 PM  #1 
Newbie Joined: Dec 2009 Posts: 2 Thanks: 0  network link state calculus
hi, if i have a network state like; a <> b (a connect to b) b <> c c <> d the represantation can be a matrix  1 1 0 0   0 1 1 0   0 0 1 1   0 0 0 1  how can i quick check if a is connected to d , by a matrix transform ? cheers. 
December 4th, 2009, 03:42 PM  #2 
Senior Member Joined: Jan 2009 From: Japan Posts: 192 Thanks: 0  Re: network link state calculus
If your adjacency matrix is Q (you give on example of this), then Q^n will be nonzero at (i, j) if there is a walk of length n from i to j. If you don't care what length it is, then for n nodes with an adjacency matrix Q, just use Q^n. This is not, in general, the most efficient way to do so, but you asked about matrix transforms.

December 6th, 2009, 02:28 PM  #3 
Newbie Joined: Dec 2009 Posts: 2 Thanks: 0  Re: network link state calculus
Hi, thanks for the answer; what is the most efecient method than? fc 
December 6th, 2009, 02:41 PM  #4 
Senior Member Joined: Jan 2009 From: Japan Posts: 192 Thanks: 0  Re: network link state calculus
It depends on what the nature of your data is (sparse? dense? acyclic? antisymmetric?), what you'll be doing with it, how many times it will change, how many searches you'll do, and so on. There is no universal "best". For most situations, though, breadthfirstsearch or depthfirstsearch will give you better speed than matrix multiplication.


Tags 
calculus, link, network, state 
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