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MathGroup Archive 2008

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Graph Theory / Cycle Matrix

  • To: mathgroup at smc.vnet.net
  • Subject: [mg92370] Graph Theory / Cycle Matrix
  • From: Fabian <fabian.uriarte at gmail.com>
  • Date: Mon, 29 Sep 2008 07:08:13 -0400 (EDT)

Dear Group-

In Mathematica 6, given a graph, spanning tree, and cotree:

<< Combinatorica`
g = GridGraph[3, 2, 2];
tree = BreadthFirstTraversal[g, 1, Tree];
cotree = FromUnorderedPairs[Complement[Edges[g], Edges[tree]]];
{GraphPlot[g], GraphPlot[tree], GraphPlot[cotree]}

is there a way to extract the list of "all" fundamental cycles for the
given twigs and links (chords)?

what is ultimately desired is [B] (i.e., various names -> the loop-
incidence matrix, cycle matrix, tieset matrix, loop matrix, etc).

Thank you group


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