Re: RDF Graphs

Hugh- I think it is safe to say that there is at least one mathematical 
graph associated with every RDF graph. Depending on what you plan to use 
it for, such a mathematical graph could be defined in more than one 
way.  Here is how I like to think of it:

It is a directed graph. It is a vertex-labelled graph, assuming you 
generate explicit names for implicit blank nodes. It also has an 
interesting property, in that every edge is "associated" with exactly 
one vertex.
* The vertices that are the tails of some edge are subjects of the RDF 
graph.
* The vertices that are the heads of some edge are objects of the RDF 
graph.
* The vertices that are associated with the edges are the predicates of 
the RDF graph.

There is no restriction on how many of these roles a vertex may assume - 
it may be simultaneously of a tail of some edge, a head of some edge and 
"associated" with an edge as a predicate. However, each vertex must play 
at least one of these roles.

Refining this further, the vertices can be restricted by their labels:
* if the vertex has a blank node label, then it cannot be associated 
with an edge.
* if a vertex is a literal, it can only be a head of an edge.

Tara


On 10/27/14, 7:04 PM, Hugh Glaser wrote:
> Thanks Peter, that’s so helpful and succinct I can get rid of the history!
>
>> On 27 Oct 2014, at 22:52, Peter F. Patel-Schneider<pfpschneider@gmail.com>  wrote:
>>
>> I don't see why you should worry about an RDF graph not being exactly a simple graph.  There are lots of situations where modifiers are not subsective.
> There are two reasons in Maths to use a term, I think.
> One of them is to appeal to some pre-defined idea of the structure of things, so that the structure under discussion can be communicated quickly.
> The other is to then appeal to a pre-existing body go knowledge about such structures.
>
>> For example, a directed graph is not exactly a graph.
> True, but all directed graphs are graphs; so using the term “graph in “directed graph” is helpful - it conveys structure by referring to previously understood things, and also allows me to lean on other Graph Theory results.
>> What counts is that an RDF graph can be considered to like a sort of a graph, and it is.
> Ah, so what “sort of graph”?
>> The normal definition of a graph is a pair consisting of a set of nodes and a set of edges, so there is no problem with saying that an RDF graph is defined as a set of triples.
> Only if you can establish the correspondence between a set of triples and a graph.
>> Mathematics is full of cases where new notions are defined by modifying or extending old ones.
> Yes, but usually only when helpful, as above.
>
> Does it help to communicate what RDF looks like?
> Well sometimes, but it also misleads, as I said.
> Can it use existing results from Graph Theory? - well (I think?) only if it has certain, characteristics, which I think are actually quite unsual.
>> peter
> Cheers
> Hugh
>

Received on Tuesday, 28 October 2014 01:11:44 UTC