collateVertices -- convert a mixed graph into a new mixed graph where each component subgraph has the same set of vertices

Synopsis

Usage:

collateVertices(G)
Inputs:
- G, an instance of the type MixedGraph,
Outputs:
- an instance of the type MixedGraph,

Description

Let G=mixedGraph(U,D,B) and denote the vertices of U by V1, the vertices of D by V2 and the vertices of B by V3. Then the method collateVertices(G) outputs a mixedGraph with same edges as before but with V1 \cup V2 \cup V3 as the vertices of U,D and B.

i1 : U = graph{{1,2},{2,3},{3,4},{1,4},{1,5}}

o1 = Graph{1 => {2, 4, 5}}
           2 => {1, 3}
           3 => {2, 4}
           4 => {1, 3}
           5 => {1}

o1 : Graph

i2 : D = digraph{{2,1},{3,1},{7,8}}

o2 = Digraph{1 => {} }
             2 => {1}
             3 => {1}
             7 => {8}
             8 => {}

o2 : Digraph

i3 : B = bigraph{{1,5}}

o3 = Bigraph{1 => {5}}
             5 => {1}

o3 : Bigraph

i4 : G = mixedGraph(U,D,B)

o4 = MixedGraph{Bigraph => Bigraph{1 => {5}}  }
                                   5 => {1}
                Digraph => Digraph{1 => {} }
                                   2 => {1}
                                   3 => {1}
                                   7 => {8}
                                   8 => {}
                Graph => Graph{1 => {2, 4, 5}}
                               2 => {1, 3}
                               3 => {2, 4}
                               4 => {1, 3}
                               5 => {1}

o4 : MixedGraph

i5 : collateVertices G

o5 = MixedGraph{Bigraph => Bigraph{1 => {5}}  }
                                   2 => {}
                                   3 => {}
                                   4 => {}
                                   5 => {1}
                                   7 => {}
                                   8 => {}
                Digraph => Digraph{1 => {} }
                                   2 => {1}
                                   3 => {1}
                                   4 => {}
                                   5 => {}
                                   7 => {8}
                                   8 => {}
                Graph => Graph{1 => {2, 4, 5}}
                               2 => {1, 3}
                               3 => {2, 4}
                               4 => {1, 3}
                               5 => {1}
                               7 => {}
                               8 => {}

o5 : MixedGraph

Ways to use collateVertices :

collateVertices(MixedGraph)

For the programmer

The object collateVertices is a method function.