graphs / design decision, eins, zwei oder drei

On Wed, 26 Feb 2003, Yannick Versley wrote:

> > Now, what is
> > subst(2,1,g);
> > supposed to do:
> >
> > 1. hypergraph([1,2,3],[[[1,2],2],[[1,3],2],[[2,3],2]],True)
> > (only edge weights are affected)
> >
> > 2. hypergraph([1,2,3],[[[2,2],2],[[2,3],2],[[2,3],2]],True)
> > (edge weights and the vertex names the edges consist of)
> >
> > 3. hypergraph([2,3],[[[2,2],2],[[2,3],2],[[2,3],2]],True)
> > (vertex names and edge weights)???
> >
> > I final possibility would be to *require* that vertex names are always
> > strings and implement 3.
> >
> > I think that 3 is most consistent with usual maxima behaviour, so it is
> > probably the right thing to do...
> 
> I think (2) is unlogical, so it would be either (1),(3) or only the vertex
> names and no edge weights (that would make sense because you could subst
> one graph into an isomorphic one).

only vertex names doesn't work because surely we want to have the edge 
weights evaluated... (you dont want an edge weight of 5-4, do you?
 
> If you require vertex names to be strings, you would have the problem you
> wanted to avoid as soon as you use strings as edge weights (yes, they
> wouldn't be weights then, but edge labels.)

not quite, because the degree of a vertex could then be "hi"+"you"... I 
didn't think about edge labels yet, not much about vertex weights 
either, the latter would probably done as in

@ARTICLE{ChungLanglands,
   author = {Fan R. K. Chung and Robert P. Langlands},
   title = {A combinatorial {Laplacian} with vertex weights},
   journal = JCT-A,
   year = 1996,
   volume = 75,
   number = 2,
   pages = {316--327},
}

> I guess it would be fine to use (3) and make sure the existing functions
> that generate graphs use disjoint sets for edge weights and vertex names.

I think so too. Any more votes?

BTW: if you'd actually USE it, please tell me so!

Thanks, Martin