[topicmapmail] graphic language for describing TopicMaps

[Thomas B. Passin]

Murray Altheim wrote:

> My understanding of hypergraphs (as defined e.g., by W.T. Tuttle
> in "Graph Theory" and elsewhere) is that it is a graph containing
> a graph. This is assuming that hypergraphs and subgraphs are
> essentially the same thing viewed from opposite sides of a mirror.
> 
> I don't see that the number of topics in an association would
> constitute a hypergraph. It can still be considered as one, flat
> graph structure. 

Not being very familiar with the term, I looked it up in FOLDOC -

http://www.nist.gov/dads/HTML/hypergraph.html

If you neglect the roles, an association might fit.  According to 
FOLDOC, a hypergraph is a pair (V, E), where V is a set of vertices and 
E is a set of hyperedges between the vertices.  An ordinary  graph is a 
pair (v,e), where the edges and vertices are individuals.

So it seems to me that if you took the collection of role-playing topics 
as the set V, you would have a hypergraph.  How the roles fit into this, 
I don't know, and if the same topic played several roles in the 
association, that would not fit either because that topic would have to 
appear more than once, which it could not in a set.

Conclusion - an association is something like a hypergraph but not 
literally one. Just to round this off, here is a tidbit from the FOLDOC 
page -

"Note: Consider "family," a relation connecting two or more people. If 
each person is a vertex, a family hyperedge connects the father, the 
mother, and all of their children. So G = (people, family) is a hypergraph."

Cheers,

Tom P