My Math Forum network link state calculus

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 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 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.
 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? 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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