On Saturday, 5 May 2012 09:51:55 UTC, Nathann Cohen wrote: > > Hellooooooooo everybody !!! > > Being lost in a foreign country, my hobbies get weirder and weirder. These > days I find myself playing with graph drawings because of a colleague of > mine, Thomas Connor. > > We are currently trying to plot his graphs in some meaningful way, and his > graphs are veeeerry symmetrical. Hence we would like to find a way to plot > them using the information contained in their automorphism group, using > some properties we think of along the way. Hence, this email : would anyone > here happen to have examples of nice symmetrical graphs which have nice > representations ? What we actually need right now (besides good ideas for a > plotting heuristic) is a collection of some graph to test it on. If you > have some you like, could you please tell me how to build them through Sage > ? If we finally get anywhere we will send you back nice pictures to get > your advice on the drawings produced ! >
For very symmetric (say, vertex and edge-transitive) graphs a meaningful way to draw would be what is called variously a collapsed adjacency matrix, a distance distribution diagram, etc. That is, you take a meaningful subgroup H, like the stabilizer of a vertex, of the automorphism group, and basically create a weighted graph, with multiple arcs, with vertices being orbits of H on vertices, and joining these new vertices with bi-weighted edges; e.g. for the Petersen graph such a diagram would look like the following: [1]-------[3]--------[6] 3 1 2 1 2 where an orbit of length k of H is denoted by [k], and the row of numbers below the diagram is indicating the (bi-)weights: as follows, from left to right: there are 3 edges going from [1] to [3], there is 1 edge going from each element of [3] to [1]; there are 2 edges going from each element of [3] to [6]; there is 1 edge going from each element of [6] to [3], and finally, there are 3 edges going from each element of [6] to [6]. In such a way one can "draw" rather huge graphs, see e.g. p.2 of http://arxiv.org/pdf/math/0012266v1.pdf Dima > > I initially asked Jason who thought some of you may be interested in the > adventure :-D > > Thaaaaaaaaaaaaaaaaaaaaaaaaaaank you for your thoughts ! ;-) > > Nathann > > P.S. : Oh, and if you already know of some code producing such drawings, > please share it ! -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org