Core Functions

Graphs.jl includes the following core functions:

Full Docs

Graphs.add_vertices! — Method
add_vertices!(g, n)

Add n new vertices to the graph g. Return the number of vertices that were added successfully.

Examples

julia> using Graphs

julia> g = SimpleGraph()
{0, 0} undirected simple Int64 graph

julia> add_vertices!(g, 2)
2
Graphs.all_neighbors — Function
all_neighbors(g, v)

Return a list of all inbound and outbound neighbors of v in g. For undirected graphs, this is equivalent to both outneighbors and inneighbors.

Implementation Notes

Returns a reference to the current graph's internal structures, not a copy. Do not modify result. If the graph is modified, the behavior is undefined: the array behind this reference may be modified too, but this is not guaranteed.

Examples

```jldoctest julia> using Graphs

julia> g = DiGraph(3);

julia> add_edge!(g, 2, 3);

julia> add_edge!(g, 3, 1);

julia> all_neighbors(g, 1) 1-element Array{Int64,1}: 3

julia> all_neighbors(g, 2) 1-element Array{Int64,1}: 3

julia> all_neighbors(g, 3) 2-element Array{Int64,1}: 1 2 ```

Graphs.common_neighbors — Method
common_neighbors(g, u, v)

Return the neighbors common to vertices u and v in g.

Implementation Notes

Returns a reference to the current graph's internal structures, not a copy. Do not modify result. If the graph is modified, the behavior is undefined: the array behind this reference may be modified too, but this is not guaranteed.

Examples

julia> using Graphs

julia> g = SimpleGraph(4);

julia> add_edge!(g, 1, 2);

julia> add_edge!(g, 2, 3);

julia> add_edge!(g, 3, 4);

julia> add_edge!(g, 4, 1);

julia> add_edge!(g, 1, 3);

julia> common_neighbors(g, 1, 3)
2-element Array{Int64,1}:
 2
 4

julia> common_neighbors(g, 1, 4)
1-element Array{Int64,1}:
 3
Graphs.degree — Function
degree(g[, v])

Return a vector corresponding to the number of edges which start or end at each vertex in graph g. If v is specified, only return degrees for vertices in v. For directed graphs, this value equals the incoming plus outgoing edges. For undirected graphs, it equals the connected edges.

Examples

julia> using Graphs

julia> g = DiGraph(3);

julia> add_edge!(g, 2, 3);

julia> add_edge!(g, 3, 1);

julia> degree(g)
3-element Array{Int64,1}:
 1
 1
 2
Graphs.degree_histogram — Method
degree_histogram(g, degfn=degree)

Return a Dict with values representing the number of vertices that have degree represented by the key.

Degree function (for example, indegree or outdegree) may be specified by overriding degfn.

Graphs.density — Function
density(g)

Return the density of g. Density is defined as the ratio of the number of actual edges to the number of possible edges ($|V|×(|V|-1)$ for directed graphs and $\frac{|V|×(|V|-1)}{2}$ for undirected graphs).

Graphs.has_self_loops — Method
has_self_loops(g)

Return true if g has any self loops.

Examples

julia> using Graphs

julia> g = SimpleGraph(2);

julia> add_edge!(g, 1, 2);

julia> has_self_loops(g)
false

julia> add_edge!(g, 1, 1);

julia> has_self_loops(g)
true
Graphs.indegree — Method
indegree(g[, v])

Return a vector corresponding to the number of edges which end at each vertex in graph g. If v is specified, only return degrees for vertices in v.

Examples

julia> using Graphs

julia> g = DiGraph(3);

julia> add_edge!(g, 2, 3);

julia> add_edge!(g, 3, 1);

julia> indegree(g)
3-element Array{Int64,1}:
 1
 0
 1
Graphs.is_ordered — Method
is_ordered(e)

Return true if the source vertex of edge e is less than or equal to the destination vertex.

Examples

julia> using Graphs

julia> g = DiGraph(2);

julia> add_edge!(g, 2, 1);

julia> is_ordered(first(edges(g)))
false
Graphs.neighbors — Method
neighbors(g, v)

Return a list of all neighbors reachable from vertex v in g. For directed graphs, the default is equivalent to outneighbors; use all_neighbors to list inbound and outbound neighbors.

Implementation Notes

Returns a reference to the current graph's internal structures, not a copy. Do not modify result. If the graph is modified, the behavior is undefined: the array behind this reference may be modified too, but this is not guaranteed.

Examples

julia> using Graphs

julia> g = DiGraph(3);

julia> add_edge!(g, 2, 3);

julia> add_edge!(g, 3, 1);

julia> neighbors(g, 1)
0-element Array{Int64,1}

julia> neighbors(g, 2)
1-element Array{Int64,1}:
 3

julia> neighbors(g, 3)
1-element Array{Int64,1}:
 1
Graphs.num_self_loops — Method
num_self_loops(g)

Return the number of self loops in g.

Examples

julia> using Graphs

julia> g = SimpleGraph(2);

julia> add_edge!(g, 1, 2);

julia> num_self_loops(g)
0

julia> add_edge!(g, 1, 1);

julia> num_self_loops(g)
1
Graphs.outdegree — Method
outdegree(g[, v])

Return a vector corresponding to the number of edges which start at each vertex in graph g. If v is specified, only return degrees for vertices in v.

Examples

julia> using Graphs

julia> g = DiGraph(3);

julia> add_edge!(g, 2, 3);

julia> add_edge!(g, 3, 1);

julia> outdegree(g)
3-element Array{Int64,1}:
 0
 1
 1
Graphs.squash — Method
squash(g)

Return a copy of a graph with the smallest practical type that can accommodate all vertices.

Graphs.weights — Method
weights(g)

Return the weights of the edges of a graph g as a matrix. Defaults to Graphs.DefaultDistance.

Implementation Notes

In general, referencing the weight of a nonexistent edge is undefined behavior. Do not rely on the weights matrix as a substitute for the graph's adjacency_matrix.