Function Repository Resource:

BidirectedGraph

Modify Graph to include extraverted double edges

Contributed by: Bradley Klee

ResourceFunction["BidirectedGraph"][g]

returns graph g, styled as a bidirectional graph, by default collapsing 2-cycles into extraverted edges.

ResourceFunction["BidirectedGraph"][{e₁,e₂,…}]

returns the graph with edges e_j, styled as a bidirectional graph, by default collapsing 2-cycles into extraverted edges.

Details

The following options can be given:

Filter

True

decides whether or not to collapse 2-cycles

Examples

Basic Examples (4)

Force two-cycles from DirectedGraph to overlap:

In[1]:=

$Row[{#, Style["\[LongRightArrow]", Gray, Bold, 40], ResourceFunction["BidirectedGraph"][#, Options[#]]}] &@ DirectedGraph[ UndirectedEdge @@ # & /@ Partition[Range[3], 2, 1, 1], ImageSize -> 200]$

Out[1]=

Do not collapse edges:

In[2]:=

$Row[{#, Style["\[LongRightArrow]", Gray, Bold, 40], ResourceFunction["BidirectedGraph"][#, Options[#], "Filter" -> False]}] &@DirectedGraph[ UndirectedEdge @@ # & /@ Partition[Range[3], 2, 1, 1], ImageSize -> 200]$

Out[2]=

Instead of converting graphs, specify edges directly:

In[3]:=

$With[{edges = DirectedEdge @@ # & /@ Tuples[Range[4], 2]}, Row[{Graph[edges, ImageSize -> 200], Style["\[LongRightArrow]", Gray, Bold, 40], ResourceFunction["BidirectedGraph"][edges, ImageSize -> 200]}]]$

Out[3]=

BidirectedGraph supports four different edge specifications:

In[4]:=

With[{edges = {
UndirectedEdge[1, 4],
DirectedEdge[1, 2],
DirectedEdge[2, 1],
LeftRightArrow[2, 3],
3 -> 4,
DirectedEdge[4, 3]}},
ResourceFunction["BidirectedGraph"][edges, "Filter" -> #] & /@ {False, True}
]

Out[4]=

Possible Issues (2)

Due to hacking of Graph, edge colorings may work out incorrectly:

In[5]:=

$ResourceFunction["BidirectedGraph"][{ UndirectedEdge[1, 4], DirectedEdge[1, 2], DirectedEdge[2, 1], LeftRightArrow[2, 3], 3 -> 4, DirectedEdge[4, 3]}, "Filter" -> False, {VertexStyle -> Red, EdgeStyle -> { LeftRightArrow[_, _] -> Red, DirectedEdge[_, _] -> Green}}]$

Out[5]=

However, with more care, it is possible to get correct colorings:

In[6]:=

$With[{edges = {UndirectedEdge[1, 4], DirectedEdge[1, 2], DirectedEdge[2, 1], LeftRightArrow[2, 3], 3 -> 4, DirectedEdge[4, 3]}}, ResourceFunction["BidirectedGraph"][edges, "Filter" -> False, EdgeStyle -> MapThread[ Alternatives @@ (Cases[edges, #1[_, _]]) -> #2 &, {{DirectedEdge, LeftRightArrow, UndirectedEdge}, {Red, Green, Blue}} ]]]$