SimpleGraphConverter

This package convertes graphs between the Graphs and SimpleGraphs modules.

The Julia modules Graphs [formerly LightGraphs] and SimpleGraphs can be used for graph theory computations. Simple graphs (graphs without directions, loops, or multiple edges) are defined in both modules.

• In Graphs the datatype is SimpleGraph.
• In SimpleGraphs the data type is UndirectedGraph (which may be abbreviated UG).

This SimpleGraphConverter module helps with conversion from one type to the other.

• If g is a SimpleGraph, then UndirectedGraph(g) [or UG(g)] converts the graph to type UndirectedGraph.
• If G is an UndirectedGraph, then SimpleGraph(G) converts the graph to a SimpleGraph.

julia> using Graphs, SimpleGraphs, SimpleGraphConverter

julia> g = cycle_graph(6)
{6, 6} undirected simple Int64 graph

julia> G = UG(g)
UndirectedGraph{Int64} (n=6, m=6)

julia> G == Cycle(6)
true

julia> G = Path(9)
Path (n=9, m=8)

julia> g = SimpleGraph(G)
{9, 8} undirected simple Int64 graph

julia> g == path_graph(9)
true

The vertices of a SimpleGraph (from the Graphs module) is always a set of integers of the form {1,2,...,n}. The vertex set of an UndirectedGraph can contain arbitrary types. When converting from a SimpleGraph to an UndirectedGraph, the names of the vertices are converted to consecutive integers.

In this example, the Petersen() function returns the Petersen graph as an UndirectedGraph. The ten vertices are the two-element subsets of {1,2,3,4,5}. When we convert to a SimpleGraph, the resulting graph has ten vertices that are the integers from 1 to 10. When we convert that SimpleGraph back to an UndirectedGraph, the vertices are different (integers vs. two-element sets) from the original.

julia> using ShowSet

julia> G = Petersen()
Petersen (n=10, m=15)

julia> g = SimpleGraph(G)
{10, 15} undirected simple Int64 graph

julia> H = UG(g)
UndirectedGraph{Int64} (n=10, m=15)

julia> G == H  
false

julia> using SimpleGraphAlgorithms

julia> is_iso(G,H)   # lots of output deleted
true