# Talk:Vertex (graph theory)

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Field: Discrete mathematics

Shouldn't it be a redirect to graph (mathematics), as node (graph theory) is? AFAIK node=vertex. Googl 19:23, 11 April 2006 (UTC)

It absolutely should not be a redirect. I fixed node to point here. Cburnett 03:33, 13 April 2006 (UTC)

In my opinion, it is impossible to explain what a vertex in a graph is without explaining what a graph is. Therefore, I replaced this article with a redirect to graph (graph theory). (same for edge (graph theory) Nevertheless, every synonym of 'vertex' should redirect here. ylloh 00:47, 15 April 2006 (UTC)

The current situation is even more weird; Vertex (graph theory) contains an entire article, while Node (graph theory) redirects to graph (mathematics). I'm redirecting Node (graph theory) to this page now, but also be aware of my discussion below which overlaps this discussion. Anoko moonlight 10:22, 13 October 2007 (UTC)

## Vertex equals node?

I might be mistaken, but as I see it, vertex is often used in a different way than node. Vertex is more often used when denoting a location within a grid, as described in Vertex (geometry). If someone mentions "this vertex of this and this graph", one might easily get confused he is trying to denote the x,y location of a node. Also, I have less often heard of "leaf vertex" in the graph(/tree) literature, while leaf node is actually an existing article - and there are more of such articles. I think that the sides of edges in a graph are more often and more properly called "node", over "vertex", so I would propose renaming this article to Node (graph theory). (More evidence is that Node (networking) exists, while a network is a specialized graph, edge described itself as "a line segment joining two nodes in a graph, etc.).

The book "discrete mathematics" by Kenneth A. Ross and Charles RB Wright book uses only "vertex" though, and describes that node is more often used in the context of (binary) trees, quote: Wat makes the search procedure work and gives the tree its "binary" name is the fact that at each vertex [or node, as they are frequently called in this setting] ...

Whatever we chose, it should be used consequent (consistently?) in my opinion, so either rename leaf node to leaf vertex, and all other pages that refer to a point of an graph edge as "vertex", or rename this article to node (graph theory). I vote for the latter. Anoko moonlight 10:19, 13 October 2007 (UTC)

I see vertex much more commonly than node to refer to the vertices of a graph, so I think the name of this article should stay as is. However in the context of trees, node is less uncommon than it is in graphs more generally, so I see no problem with leaf node either. —David Eppstein 14:36, 13 October 2007 (UTC)
Okay, I think you are right. Maybe we should add this information briefly to the text. Anoko moonlight 08:34, 15 October 2007 (UTC)

Comment: The opening section is very confusing, it does not say what exactly is a vertex. "the fundamental unit out of which graphs are formed". Thanks, but that was already said in Graph theory. "an undirected graph consists of a set of vertices..." It says what vertices compose (graphs), not what a vertex is.--Andrés Baldrich (talk) 21:50, 1 June 2009 (UTC)

It does too, in the next sentence: they are featureless and indivisible objects. —David Eppstein (talk) 22:29, 1 June 2009 (UTC)
Also, the article states ...' unit of which ' versus the commenter who states ...'unit out of which'.50.72.157.124 (talk) 19:17, 18 August 2013 (UTC)
I actually piped in to compliment the article, which I was able to read, comprehend, and resolve, on the first pass. Kudos to an a-political maths presentation; very refreshing.50.72.157.124 (talk) 19:17, 18 August 2013 (UTC)