Re: Do Data Models Need to built on a Mathematical Concept?

> > In general, a graph is composed of binary relations.
> > When a graph consists of only two nodes
> > it may then be equivalent to a binary relation.
>
> A binary relation is a set of ordered pairs drawn from a common domain.

My personal definition of a binary relation is 'Two things that have something in common'.

It seems your definition of a binary relation above is quite similar. I believe mine is simpler and more accurate because it is the more general form and based on fewer things. In your definition, one would need to define additional things such as set, order, pair, drawn and domain.

> A graph G can be viewed as a set of ordered pairs (Vertice, Edge)
> where Edge is itself a set of ordered pairs (Vertice, Vertice).

I will concede, it is true that a human can view a graph as a set of ordered pair (nodes, links) in his mind, but to do so, he is utilizing information that is out of the universe of discourse. The universe of discourse is simply the graph itself and does not include information being utilized by the human to create the ordered pair (Nodes, Links).

For example, lets say we have 3 nodes linked in a triangle. Thus you are saying

Graph = (Nodes, Links)
Nodes = (1, 2, 3)
Links = ((1,2), (2,3), (3,1))

Now you point out "Graph = (Nodes, Links)" and say there is the binary relation.
Yes, that is, but, a human is creating that with additional information in his brain and that information is not in the graph itself.

A human views the three nodes and says, hey they all look like balls, so I can think of them as being similar, but no data is encoded in the graph itself that shows a commonality between them.

A human views the three links and says, hey they look like lines, so I can think of them as being similar, but here again, no data is encoded in the graph itself that shows a commonality between links.

Note, a drawing of the graph does encode info, but that info is not in the graph itself. Ask yourself, is the graph itself providing the commonality between things or is it yourself?

As I said before and say again, the graph itself is not A binary relation, it is composed OF multiple binary relations. Received on Sun May 04 2003 - 22:40:40 CEST