Is a loop (in graph theory) considered adjacent to itself?

Question

Is a loop (in graph theory) considered adjacent to itself? Neither my textbook nor pure math associates seem to have a sure answer. for example:: in an exercise, there is a graph displayed containing a vertex v with a loop e, and other edges incident on v. The question asks, which edges are adjacent to e?

Answer 1

The formal definition in my textbook is "Two edges are adjacent if they are both incident on the same vertex." As seems clear both in this definition and in the comments, we are agreed that this is an irreflexive relation. Since all loops are edges, our agreement is therefore that a loop cannot be adjacent to itself.

If your follow-up question is "Loops are a special sort of edge; will this harsh definition of adjacency cause us headaches as we continue to study graph theory?" -- I can't recall any point where it ever does in practice.