isSimple(MixedGraph) -- check whether a mixed graph is simple

Synopsis

Function: isSimple
Usage:

isSimple(G)
Inputs:
- G, an instance of the type MixedGraph,
Outputs:
- a Boolean value,

Description

This method checks whether a graph is simple: does not contain loops or multiple edges. Note that since graph, digraph and bigraph do not allow multiple edges, a graph of class MixedGraph can only have multiple edges of different types.

In the following example, there are no loops or multiple edges.

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 : isSimple G

o5 = true

This example contains multiple edges on vertices 1 and 2.

i6 : U = graph{{1,2},{2,3},{3,4}}

o6 = Graph{1 => {2}   }
           2 => {1, 3}
           3 => {2, 4}
           4 => {3}

o6 : Graph

i7 : D = digraph{{1,2},{2,5}}

o7 = Digraph{1 => {2}}
             2 => {5}
             5 => {}

o7 : Digraph

i8 : B = bigraph{{5,6}}

o8 = Bigraph{5 => {6}}
             6 => {5}

o8 : Bigraph

i9 : G = mixedGraph(U,D,B)

o9 = MixedGraph{Bigraph => Bigraph{5 => {6}}}
                                   6 => {5}
                Digraph => Digraph{1 => {2}}
                                   2 => {5}
                                   5 => {}
                Graph => Graph{1 => {2}   }
                               2 => {1, 3}
                               3 => {2, 4}
                               4 => {3}

o9 : MixedGraph

i10 : isSimple G

o10 = false

This example contains a loop.

i11 : U = graph{{1,2},{2,3},{3,4}}

o11 = Graph{1 => {2}   }
            2 => {1, 3}
            3 => {2, 4}
            4 => {3}

o11 : Graph

i12 : D = digraph{{2,5}}

o12 = Digraph{2 => {5}}
              5 => {}

o12 : Digraph

i13 : B = bigraph{{5,6},{5,5}}

o13 = Bigraph{5 => {5, 6}}
              6 => {5}

o13 : Bigraph

i14 : G = mixedGraph(U,D,B)

o14 = MixedGraph{Bigraph => Bigraph{5 => {5, 6}}}
                                    6 => {5}
                 Digraph => Digraph{2 => {5}}
                                    5 => {}
                 Graph => Graph{1 => {2}   }
                                2 => {1, 3}
                                3 => {2, 4}
                                4 => {3}

o14 : MixedGraph

i15 : isSimple G

o15 = false

Ways to use this method: