loop LoopOfAGraph 2002-01-25 18:04:24 2003-08-21 04:13:15 Definition graph \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \PMlinkescapeword{joins} \PMlinkescapeword{contain} In graph theory, a \emph{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 \emph{loop} is a quasigroup which contains an identity element.