# signed graphs

Can signed graphs be handled by sage ?

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You can assign weights or labels to edges, so you can have signs that way. I don't know of specific support for signed graphs beyond that. You're welcome to extend things with functions for signed graphs, though!

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What do you mean by handled? You can make a graph with edge weights in 1,-1:

sage: m = random_matrix(QQ, 5,5, num_bound=1, den_bound=1,density=0.75)
sage: m
[-1  0  0  1  1]
[ 1  0  0  1  0]
[ 0  0  0  1 -1]
[ 0  1  0  1  1]
[ 1  0  1  0  0]
sage: G
Looped graph on 5 vertices
sage: G.edges()
[(0, 0, -1), (0, 3, 1), (0, 4, 1), (1, 3, 1), (2, 3, 1), (2, 4, -1), (3, 3, 1), (3, 4, 1)]
sage: G.weighted()
True
sage: G.incidence_matrix()
[-1 -1  0  0  0  0  0  1]
[ 0  0 -1  0  0  0  0  0]
[ 0  0  0 -1 -1  0  0  0]
[ 0  1  1  0  1 -1  1  0]
[ 1  0  0  1  0  1  0  0]

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Though according to http://en.wikipedia.org/wiki/Signed_graph#Other_kinds_of_.22signed_graph.22, these are not quite the same thing because of the additional multiplicative structure...

( 2011-11-01 12:39:40 +0200 )edit

Ah, I see. It wouldn't be too hard to subclass a graph to add the signed graph-specific functionality, ISTM.

( 2011-11-01 15:19:08 +0200 )edit

Of course.

( 2011-11-01 22:04:45 +0200 )edit