Definition talk:Multigraph

Other Definitions
This definition of multigraph is a limited one, based on the definition of multiset. As currently defined here, a multigraph can be represented as a weighted graph whose weights are natural numbers. This appears to be a valid use of the term "multigraph", but it is limited: edges have multiplicity, but not identity. Thus one cannot speak sensibly of distinct length-$1$ walks from vertex $a$ to vertex $b$, and it might be necessary to adjust the notion of "cycle" in this context. That is, a multigraph with vertices $a,b$ and edge $\{a,b\}$ of multiplicity $2$ would be considered to have a cycle $(a,b,a)$, I believe, although by our definitions there is no path from $a$ to $a$. Obviously this whole area of is very limited, and as someone who knows virtually nothing about graph theory I am not the one to fix that, but I would love to get enough together to be able to deal with König's Lemma, which is more set theory than graph theory. --Dfeuer (talk) 16:33, 29 May 2013 (UTC)