Graph Theory - Pathset and Cutset determination

*To*: mathgroup at smc.vnet.net*Subject*: [mg108953] Graph Theory - Pathset and Cutset determination*From*: Robert Wright <mathematicauser1 at yahoo.com>*Date*: Thu, 8 Apr 2010 08:01:00 -0400 (EDT)

I've been playing with Mathematica's GraphUtilities` and Combinatorica` packages and wonder whether they can help me tackle the problem of calculating the minimal pathsets and minimal cutsets for a graph network. In my case, there's more than one minimal pathset/cutset and I need to identify them all. There seem to be a few hurdles, so I am looking for advice from those who have crossed the same bridges! 1. It looks like WRI are looking to replace the functionality of Combinatorica with the GraphUtilities package - is that correct? If so am I better off sticking with the Wolfram version which is hopefully still in development. The list-of-rules approach, i.e. {1->2, 2->4.... x->y} etc, used by WRI makes more sense to me but there are fewer algorithms and functions in GraphUtilities. 2. The Mathematica Help documentation gives minimal explanation for the functions in both packages: should I buy the Combinatorica book? 3. Is there a good round level up text on Graph Theory aimed at real world applications and if so what would you recommend I look at or buy. (I hear the Combinatorica book by Sriram Pemmaraju and Steven Skena is mainly a description of what Combinatorica does as opposed to the principles underlying Graph Theory and its applications. All thoughts welcome.