# Operators

Graphs.jl implements the following graph operators. In general, functions with two graph arguments will require them to be of the same type (either both SimpleGraph or both SimpleDiGraph).

## Full docs

Base.intersectMethod
intersect(g, h)

Return a graph with edges that are only in both graph g and graph h.

Implementation Notes

This function may produce a graph with 0-degree vertices. Preserves the eltype of the input graph.

Examples

julia> using Graphs

julia> g1 = SimpleDiGraph([0 1 0 0 0; 0 0 1 0 0; 1 0 0 1 0; 0 0 0 0 1; 0 0 0 1 0]);

julia> g2 = SimpleDiGraph([0 1 0; 0 0 1; 1 0 0]);

julia> foreach(println, edges(intersect(g1, g2)))
Edge 1 => 2
Edge 2 => 3
Edge 3 => 1
source
Base.joinMethod
join(g, h)

Return a graph that combines graphs g and h using blockdiag and then adds all the edges between the vertices in g and those in h.

Implementation Notes

Preserves the eltype of the input graph. Will error if the number of vertices in the generated graph exceeds the eltype.

Examples

julia> using Graphs

julia> g = join(star_graph(3), path_graph(2))
{5, 9} undirected simple Int64 graph

julia> collect(edges(g))
9-element Vector{Graphs.SimpleGraphs.SimpleEdge{Int64}}:
Edge 1 => 2
Edge 1 => 3
Edge 1 => 4
Edge 1 => 5
Edge 2 => 4
Edge 2 => 5
Edge 3 => 4
Edge 3 => 5
Edge 4 => 5
source
Base.reverseFunction
reverse(g)

Return a directed graph where all edges are reversed from the original directed graph.

Implementation Notes

Preserves the eltype of the input graph.

Examples

julia> using Graphs

julia> g = SimpleDiGraph([0 1 0 0 0; 0 0 1 0 0; 1 0 0 1 0; 0 0 0 0 1; 0 0 0 1 0]);

julia> foreach(println, edges(reverse(g)))
Edge 1 => 3
Edge 2 => 1
Edge 3 => 2
Edge 4 => 3
Edge 4 => 5
Edge 5 => 4
source
Base.sizeMethod
size(g, i)

Return the number of vertices in g if i=1 or i=2, or 1 otherwise.

Examples

julia> using Graphs

julia> g = cycle_graph(4);

julia> size(g, 1)
4

julia> size(g, 2)
4

julia> size(g, 3)
1
source
Base.sumMethod
sum(g, i)

Return a vector of indegree (i=1) or outdegree (i=2) values for graph g.

Examples

julia> using Graphs

julia> g = SimpleDiGraph([0 1 0 0 0; 0 0 1 0 0; 1 0 0 1 0; 0 0 0 0 1; 0 0 0 1 0]);

julia> sum(g, 2)
5-element Vector{Int64}:
1
1
2
1
1

julia> sum(g, 1)
5-element Vector{Int64}:
1
1
1
2
1
source
Base.sumMethod
sum(g)

Return the number of edges in g.

Examples

julia> using Graphs

julia> g = SimpleGraph([0 1 0; 1 0 1; 0 1 0]);

julia> sum(g)
2
source
Base.unionMethod
union(g, h)

Return a graph that combines graphs g and h by taking the set union of all vertices and edges.

Implementation Notes

Preserves the eltype of the input graph. Will error if the number of vertices in the generated graph exceeds the eltype.

Examples

julia> using Graphs

julia> g = SimpleGraph(3); h = SimpleGraph(5);

julia> f = union(g, h);

julia> collect(edges(f))
5-element Vector{Graphs.SimpleGraphs.SimpleEdge{Int64}}:
Edge 1 => 2
Edge 1 => 3
Edge 3 => 4
Edge 3 => 5
Edge 4 => 5
source
Graphs.cartesian_productMethod
cartesian_product(g, h)

Return the cartesian product of g and h.

Implementation Notes

Preserves the eltype of the input graph. Will error if the number of vertices in the generated graph exceeds the eltype.

Examples

julia> using Graphs

julia> g = cartesian_product(star_graph(3), path_graph(3))
{9, 12} undirected simple Int64 graph

julia> collect(edges(g))
12-element Vector{Graphs.SimpleGraphs.SimpleEdge{Int64}}:
Edge 1 => 2
Edge 1 => 4
Edge 1 => 7
Edge 2 => 3
Edge 2 => 5
Edge 2 => 8
Edge 3 => 6
Edge 3 => 9
Edge 4 => 5
Edge 5 => 6
Edge 7 => 8
Edge 8 => 9
source
Graphs.complementMethod
complement(g)

Return the graph complement of a graph

Implementation Notes

Preserves the eltype of the input graph.

Examples

julia> using Graphs

julia> g = SimpleDiGraph([0 1 0 0 0; 0 0 1 0 0; 1 0 0 1 0; 0 0 0 0 1; 0 0 0 1 0]);

julia> foreach(println, edges(complement(g)))
Edge 1 => 3
Edge 1 => 4
Edge 1 => 5
Edge 2 => 1
Edge 2 => 4
Edge 2 => 5
Edge 3 => 2
Edge 3 => 5
Edge 4 => 1
Edge 4 => 2
Edge 4 => 3
Edge 5 => 1
Edge 5 => 2
Edge 5 => 3
source
Graphs.compute_shiftsMethod
compute_shifts(n::Int, x::AbstractArray)

Determine how many elements of x are less than i for all i in 1:n.

source
Graphs.crosspathFunction
crosspath(len::Integer, g::Graph)

Return a graph that duplicates g len times and connects each vertex with its copies in a path.

Implementation Notes

Preserves the eltype of the input graph. Will error if the number of vertices in the generated graph exceeds the eltype.

Examples

julia> using Graphs

julia> g = crosspath(3, path_graph(3))
{9, 12} undirected simple Int64 graph

julia> collect(edges(g))
12-element Vector{Graphs.SimpleGraphs.SimpleEdge{Int64}}:
Edge 1 => 2
Edge 1 => 4
Edge 2 => 3
Edge 2 => 5
Edge 3 => 6
Edge 4 => 5
Edge 4 => 7
Edge 5 => 6
Edge 5 => 8
Edge 6 => 9
Edge 7 => 8
Edge 8 => 9
source
Graphs.differenceMethod
difference(g, h)

Return a graph with edges in graph g that are not in graph h.

Implementation Notes

Note that this function may produce a graph with 0-degree vertices. Preserves the eltype of the input graph.

Examples

julia> using Graphs

julia> g1 = SimpleDiGraph([0 1 0 0 0; 0 0 1 0 0; 1 0 0 1 0; 0 0 0 0 1; 0 0 0 1 0]);

julia> g2 = SimpleDiGraph([0 1 0; 0 0 1; 1 0 0]);

julia> foreach(println, edges(difference(g1, g2)))
Edge 3 => 4
Edge 4 => 5
Edge 5 => 4
source
Graphs.egonetMethod
egonet(g, v, d, distmx=weights(g))

Return the subgraph of g induced by the neighbors of v up to distance d, using weights (optionally) provided by distmx. This is equivalent to induced_subgraph(g, neighborhood(g, v, d, dir=dir))[1].

Optional Arguments

• dir=:out: if g is directed, this argument specifies the edge direction

with respect to v (i.e. :in or :out).

source
Graphs.induced_subgraphMethod
induced_subgraph(g, vlist)
induced_subgraph(g, elist)

Return the subgraph of g induced by the vertices in vlist or edges in elist along with a vector mapping the new vertices to the old ones (the vertex i in the subgraph corresponds to the vertex vmap[i] in g.)

The returned graph has length(vlist) vertices, with the new vertex i corresponding to the vertex of the original graph in the i-th position of vlist.

Usage Examples

julia> g = complete_graph(10)

julia> sg, vmap = induced_subgraph(g, 5:8)

julia> @assert g[5:8] == sg

julia> @assert nv(sg) == 4

julia> @assert ne(sg) == 6

julia> @assert vm[4] == 8

julia> sg, vmap = induced_subgraph(g, [2,8,3,4])

julia> @assert sg == g[[2,8,3,4]]

julia> elist = [Edge(1,2), Edge(3,4), Edge(4,8)]

julia> sg, vmap = induced_subgraph(g, elist)

julia> @assert sg == g[elist]
source
Graphs.merge_vertices!Method
merge_vertices!(g, vs)

Combine vertices specified in vs into single vertex whose index will be the lowest value in vs. All edges connected to vertices in vs connect to the new merged vertex.

Return a vector with new vertex values are indexed by the original vertex indices.

Implementation Notes

Supports SimpleGraph only.

Examples

julia> using Graphs

julia> g = path_graph(5);

julia> collect(edges(g))
4-element Vector{Graphs.SimpleGraphs.SimpleEdge{Int64}}:
Edge 1 => 2
Edge 2 => 3
Edge 3 => 4
Edge 4 => 5

julia> merge_vertices!(g, [2, 3])
5-element Vector{Int64}:
1
2
2
3
4

julia> collect(edges(g))
3-element Vector{Graphs.SimpleGraphs.SimpleEdge{Int64}}:
Edge 1 => 2
Edge 2 => 3
Edge 3 => 4
source
Graphs.merge_verticesMethod
merge_vertices(g::AbstractGraph, vs)

Create a new graph where all vertices in vs have been aliased to the same vertex minimum(vs).

Examples

julia> using Graphs

julia> g = path_graph(5);

julia> collect(edges(g))
4-element Vector{Graphs.SimpleGraphs.SimpleEdge{Int64}}:
Edge 1 => 2
Edge 2 => 3
Edge 3 => 4
Edge 4 => 5

julia> h = merge_vertices(g, [2, 3]);

julia> collect(edges(h))
3-element Vector{Graphs.SimpleGraphs.SimpleEdge{Int64}}:
Edge 1 => 2
Edge 2 => 3
Edge 3 => 4
source
Graphs.symmetric_differenceMethod
symmetric_difference(g, h)

Return a graph with edges from graph g that do not exist in graph h, and vice versa.

Implementation Notes

Note that this function may produce a graph with 0-degree vertices. Preserves the eltype of the input graph. Will error if the number of vertices in the generated graph exceeds the eltype.

Examples

julia> using Graphs

julia> g = SimpleGraph(3); h = SimpleGraph(3);

julia> f = symmetric_difference(g, h);

julia> collect(edges(f))
3-element Vector{Graphs.SimpleGraphs.SimpleEdge{Int64}}:
Edge 1 => 2
Edge 1 => 3
Edge 2 => 3
source
Graphs.tensor_productMethod
tensor_product(g, h)

Return the tensor product of g and h.

Implementation Notes

Preserves the eltype of the input graph. Will error if the number of vertices in the generated graph exceeds the eltype.

Examples

julia> using Graphs

julia> g = tensor_product(star_graph(3), path_graph(3))
{9, 8} undirected simple Int64 graph

julia> collect(edges(g))
8-element Vector{Graphs.SimpleGraphs.SimpleEdge{Int64}}:
Edge 1 => 5
Edge 1 => 8
Edge 2 => 4
Edge 2 => 6
Edge 2 => 7
Edge 2 => 9
Edge 3 => 5
Edge 3 => 8
source
SparseArrays.blockdiagMethod
blockdiag(g, h)

Return a graph with $|V(g)| + |V(h)|$ vertices and $|E(g)| + |E(h)|$ edges where the vertices and edges from graph h are appended to graph g.

Implementation Notes

Preserves the eltype of the input graph. Will error if the number of vertices in the generated graph exceeds the eltype.

Examples

julia> using Graphs

julia> g1 = SimpleDiGraph([0 1 0 0 0; 0 0 1 0 0; 1 0 0 1 0; 0 0 0 0 1; 0 0 0 1 0]);

julia> g2 = SimpleDiGraph([0 1 0; 0 0 1; 1 0 0]);

julia> blockdiag(g1, g2)
{8, 9} directed simple Int64 graph

julia> foreach(println, edges(blockdiag(g1, g2)))
Edge 1 => 2
Edge 2 => 3
Edge 3 => 1
Edge 3 => 4
Edge 4 => 5
Edge 5 => 4
Edge 6 => 7
Edge 7 => 8
Edge 8 => 6
source