In graph theory, a loop is an edge which joins a vertex to itself, rather than to some other vertex. By definition, a graph cannot contain a loop; a pseudograph, however, may contain both multiple edges and multiple loops. Note that by some definitions, a multigraph may contain multiple edges and no loops, while other texts define a multigraph as a graph allowing multiple edges and multiple loops.

In algebra, a loop is a quasigroup which contains an identity element.