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Topic: graph theory (Read 725 times) |
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mathelete
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graph theory
« on: Mar 27th, 2005, 10:17am » |
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Can anybody tell me about the properties of the real (may be negative) weighted adjacency matrix of a graph.
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towr
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Re: graph theory
« Reply #1 on: Mar 27th, 2005, 12:45pm » |
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I don't see any reason why it should have any properties besides those any square matrix has.. (i.e. being square  )
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| « Last Edit: Mar 27th, 2005, 12:46pm by towr » |
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iyerkri
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Re: graph theory
« Reply #2 on: Mar 27th, 2005, 1:33pm » |
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isn't it symmetric too??...
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towr
wu::riddles Moderator
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Re: graph theory
« Reply #3 on: Mar 27th, 2005, 1:55pm » |
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Only if the graph is. i.e. it's not directed.
Otherwise you could for instance have nodes A and B, and it costs 0.5 to go from A to B, and 0.9 to go from B to A (or other arbityary values)
Aside from symmetry, the only other relational property of graphs I can think up that you can recognize from the matrix is reflexivity.
i.e. Iff the diagonal elements of the matrix are all non-zero then the graph is reflexive.
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| « Last Edit: Mar 27th, 2005, 1:56pm by towr » |
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