What is a loop in graph theory?

In graph theory, a loop specifically refers to an edge that connects a vertex to itself. This means that a loop does not connect two different vertices as traditional edges do, but instead it starts and ends at the same vertex. Loops are significant in various applications of graph theory, particularly in modeling situations where a vertex has a relationship with itself, such as in certain network and circuit configurations. This particular characteristic of a loop is what distinguishes it from other types of edges or paths in a graph.

Other options describe different concepts: an edge connecting two different vertices is simply called an edge; a path that circles back to the starting point refers to a cycle in graph theory; and directed edges pertain to edges that have a specific direction from one vertex to another, which does not directly relate to loops. Hence, the definition of a loop is unique and specifically aligns with option B.