JA: I will be making some comments on the variations in definitions and terminology, but just to keep my headings together I will locate everything on the Graph theory talk page. A given undirected graph can be oriented in different ways but these lead to different oriented graphs, not to the same oriented graph where the orientation has "varied". It seems to me that an oriented graph consists of a pair (undirected graph, orientation). I question this: "A more fundamental difference is that, in a directed graph (or multigraph), the directions are fixed, but in an oriented graph (or multigraph), only the underlying graph is fixed, while the orientation may vary." I don't know what "may vary" means. Compare (graph_theory)#Degree: "For a directed graph, a loop adds one to the in degree and one to the out degree." – This directly contradicts the definition on this page (x/=y). While literature may offer mutually exclusive definitions, at least the articles on Wikipedia should not contradict one another. I am surprised why a directed graph should _not_ allow self loops. The other notion is a cycle, and it's not really defined on this article (surprisingly enough).- Wgunther ( talk) 15:18, 6 October 2010 (UTC) A loop is defined in the article to be an edge from a vertex to itself. Cesiumfrog ( talk) 05:49, 1 October 2010 (UTC) I'm not sure why there would be confusion. It's one thing to have a line coming out from a node and back around directly in to the same node again. Something the article should make more clear is which of the two intuitive concepts of loop it is referring to. Whichever we give as the primary definition, the section on variations of definitions should mention the inconsistency. MathMartin 13:47, (UTC) The graph theory literature is divided on whether "digraph" allows loops. If you think you can make the definitions more consistent or clearer go ahead. At the moment I am a bit busy so I am unable to work on either article. Another reason for the broader definition is to define a broader notion of graph homomorphism (as you have already noticed). The broad definition can be narrowed down, if necessary, by using adjectives like simple. I think it is easier having a broad definition for graphs and digraphs which includes loops and multiple edges than giving separate definitions. Anyone else have an opinion? dbenbenn | talk 02:47, (UTC) Yes I would change the definition of graph to allow loops (my main concern is consistency too). It sounds like you think the definition of "graph" should be changed to allow loops. MathMartin 19:55, (UTC) Well, I guess I mainly care about consistency between "graph" and "directed graph".
But you are free to change the definition. In my opinion it is easier to call a graph without loops simple graph and a graph with loops graph then the other way round.
I'll make the change eventually unless there are objections. (And it did before I edited it!) I suggest that by default, a directed graph should not allow loops that possibility should only be mentioned in the alternate definitions section. The current definition of "directed graph" allows loops. MathMartin 16:22, (UTC)Īfter that he did another theory -Preceding unsigned comment added by 217.38.127.254 ( talk) 17:44, 4 September 2007 (UTC) Loops? See Wikipedia_talk:WikiProject_Mathematics#Graph_.28mathematics.29_vs_Graph_theory for a discussion. Wandrer2 09:28, 26 January 2007 (UTC) Merged graph (mathematics) into graph theory The same applies to hypergraphs and any other generalization. Of course not all matroids correspond to graphs - that's the whole point of a generalization. The previous text was this: Every graph gives rise to a matroid, but in general the graph cannot be recovered from its matroid, so matroids are not truly generalizations of graphs.