# isLoopless -- check whether a graph contains a loop

## Description

This method checks whether a graph contains a loop.

If the input is a Graph or a Bigraph, then this is equivalent to isSimple.

If the input is a Digraph, then this is equivalent to checking whether the underlyingGraph isSimple.

If the input is a MixedGraph, then this checks whether the undirected, directed and bidirected subgraphs separately contain loops.

 i1 : U = graph{{1,2},{2,3},{3,4}} o1 = Graph{1 => {2} } 2 => {1, 3} 3 => {2, 4} 4 => {3} o1 : Graph i2 : D = digraph{{2,5}} o2 = Digraph{2 => {5}} 5 => {} o2 : Digraph i3 : B = bigraph{{5,6}} o3 = Bigraph{5 => {6}} 6 => {5} o3 : Bigraph i4 : G = mixedGraph(U,D,B) o4 = MixedGraph{Bigraph => Bigraph{5 => {6}}} 6 => {5} Digraph => Digraph{2 => {5}} 5 => {} Graph => Graph{1 => {2} } 2 => {1, 3} 3 => {2, 4} 4 => {3} o4 : MixedGraph i5 : isLoopless G o5 = true
 i6 : U = graph{{1,1}} o6 = Graph{1 => {1}} o6 : Graph i7 : isLoopless U o7 = false

## Ways to use isLoopless :

• "isLoopless(Bigraph)"
• "isLoopless(Digraph)"
• "isLoopless(Graph)"
• "isLoopless(MixedGraph)"

## For the programmer

The object isLoopless is .