Talk:Handshaking lemma

I read: "every finite undirected graph has an even number of vertices with odd degree"

Why is the graph supposed undirected?

It seems to me this this lemma is also valid for directed graphs...
 * For directed graphs there may exist odd numbers of vertices with odd indegree or odd outdegree (consider the graph with one directed edge). It's true for total degree but that's essentially the same as the degree in the underlying undirected graph. —David Eppstein (talk) 15:52, 28 September 2013 (UTC)

"Vertices", "Nodes", "Vertices (or nodes)"?
The article is looking great! However, I'm looking to inquire about the consistency of "vertices, nodes, etc" Is there a Wikipedian standard for terms used in Graph Theory such that they don't get used so inconsistently? I am very used to "pick a style and apply it ad infinitum." Obviously the matter is trivial, but I do wish to know.

Cheers Tea-caff (talk) 21:24, 6 February 2023 (UTC)