|
|
MoeBlee <jazzmobe@xxxxxxxxxxx> wrote:
> I know too little about graph theory, so I have a beginner's question.
>
> An edge is an unorded pair of vertices.
>
> And I've seen ordered pairs used so that there can be two edges between
> vertex b and vertex c, one edge going in one direction and the other
> edge going in the opposite direction.
>
> But how do we rigorously define having more than two edges between
> vertex b and vertex c? In other words, how do we define what we picture
> when we draw more than two lines between vertex b and vertex c?
One standard definion for such a (directed multi)graph looks like this:
(1) a set E of edges
(2) a set V of vertices
(3) two maps s: E --> V and t: E --> V
the idea here is, that an edge e in E, s(e) is its "source" and
t(e) is its "target".
You can combine s and t to a map (s,t): E --> V x V. If this map is
injective you end up with the above special case of identifying
edges with certain ordered pairs of vertices.
Marc
|
|