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December 4th, 2009, 12:23 PM   #1
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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.
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December 4th, 2009, 03:42 PM   #2
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Re: network link state calculus

If your adjacency matrix is Q (you give on example of this), then Q^n will be non-zero 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.
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December 6th, 2009, 02:28 PM   #3
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Re: network link state calculus

Hi,
thanks for the answer;
what is the most efecient method than?


fc
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December 6th, 2009, 02:41 PM   #4
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Re: network link state calculus

It depends on what the nature of your data is (sparse? dense? acyclic? anti-symmetric?), 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, breadth-first-search or depth-first-search will give you better speed than matrix multiplication.
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