Does the term 'graph' without descriptors refer to directed or undirected?

Question

Suppose you read the word 'graph' in a paper without descriptors preceding it.

What should your default assumption be: directed or undirected?

Answer 1

The context, as always, is very important. The simplest graphs have no loops, no multiple edges, are undirected, and finite. Everything else can be built on top of that. There is no limit to how much additional structure can be built beyond the basics. It seems to me "keep it simple" is a good idea unless there is a need to add complexity for a specific purpose, and that depends on the context. Any actual use of "graph" should be enough to supply the assumptions that are used, otherwise the situation is ambiguous, which can happen, and you have to keep an open mind until the situation becomes more clear. For example, the author could mean "graph of a function" which is a very different idea and the mention of a function will almost certainly settle the matter. If the author includes a figure, then again, looking at it will almost certainly settle the matter.