NautyGraphs.jl

NautyGraphs.jl is a Julia interface to the popular graph isomorphism tool nauty by Brendan McKay. It allows for efficient isomorphism checking, canonical labeling, and hashing of vertex-labeled graphs. In addition, NautyGraphs.jl is fully compatible with the Graphs.jl API. This makes it easy to create or modify graphs through familiar syntax, and allows NautyGraphs to work with a large library of graph algorithms. Warning: NautyGraphs.jl currently does not work on Windows.

Installation

To install NautyGraphs.jl from the Julia REPL, press ] to enter Pkg mode, and then run

pkg> add NautyGraphs

Basic Usage

NautyGraphs.jl defines the NautyGraph or NautyDiGraph graph formats, which can be constructed and modified in the same way as regular Graphs from Graphs.jl:

using NautyGraphs

A = [0 1 0 0;
     1 0 1 1;
     0 1 0 1;
     0 1 1 0]
g = NautyGraph(A)

h = NautyGraph(4)
for edge in [Edge(2, 4), Edge(4, 1), Edge(4, 3), Edge(1, 3)]
  add_edge!(h, edge)
end

Internally, a NautyGraph is represented as by its adjacency matrix in a memory-efficient format, and it can be passed directly to nauty without any conversion. To check whether two graphs are isomorphic, use is_isomorphic or ≃ (\simeq):

julia> g == h
false

julia> g ≃ h
true

Use canonize!(g) to reorder g into canonical order. canonize!(g) also returns the permutation needed to canonize g:

julia> canonize!(g)
4-element Vector{Int32}:
 1
 3
 4
 2

julia> canonize!(h)
4-element Vector{Int32}:
 2
 1
 3
 4

julia> g == h
true

A sparse graph format is also available via SpNautyGraph.

See also

• nauty & traces
• Nauty.jl
• NautyTraces.jl
• Graphs.jl