Terminology in graph theory [Directed graph] 
Hi,
Have graph theorists agreed on the definitions of most of their basic objects? In particular, the definitions of "simple" and "elementary" path?
Sincerely,

P/s: I was kinda surprised learning that Germans have their own ways to define "path". And I also found that back in the 2010s, there were at least two schools of terminology for directed graphs.
(At least from what I read in [1])
[1]:

Note: There are two different definitions for "simple path". Here we follow the definition of Berge[1], Liu[2], Rosen[3] and others. A
"simple path" according to another group (Cormen et al[4], Stanat and
McAllister[5] and others) is a path in which no vertices appear more
than once.

 A: I think that there is more consistency these days than in the document you are citing, which is just over 20 years old.
A common set of definitions avoids "simple path" and "elementary path" entirely and uses the progression

*

*walk (sequence of vertices and edges)

*trail (no repeated edges)

*path (no repeated vertices)

I would not be too surprised to encounter a paper which uses "path" to mean "trail" or "walk", but the above is what I would assume by default. Regarding the notions of "walk" or "trail", there is more confusion, because the middle ground where we allow repeated vertices but no repeated edges is very rarely necessary.
If you follow one of the standard textbooks by Bollobás, or Bondy and Murty, or Diestel, or West, you will have the right notion of "path". (Out of respect for all these authors I have listed their names in alphabetical order.)
It will probably take a long time before everyone agrees on this terminology, because graph theory is a disjointed field: in addition to graph theorists studying it, there are also network theorists with their own notation, and computer scientists with their own notation, and these groups talk to each other less often than they ought to.
