Multigraphs

We provide a bare-bones implementation of multigraphs that allow loops and multiple edges.

EasyMultiGraph Constructors

Multigraphs can be created by either specifying a nonnegative integer for the number of vertices or a Graph.

EasyMultiGraph(n::Int) creates a multigraph with vertex set {1,2,...,n}.
EasyMultiGraph(g::Graph) creates a multigraph by copying g with every edge having multiplicity 1.

NOTE: Once created, the number of vertices in an EasyMultiGraph cannot be changed.

Adding/Removing Edges

To add/remove edges to a multigraph, we provide the following functions:

add!(g,u,v) adds an edge (u,v) to g [increase multiplicity by one]. May also be invoked as add!(g,(u,v)).
rem!(g,u,v) removes an edge (u,v) from g [decrease multiplicity by one]. May also be invoked as rem(g,(u,v)).

These functions return true if successful. They return false if either u or v is invalid. The rem! function also returns false if no (u,v) edge is present in g.

The order in which u and v are given is irrelevant.

Basic Operations

nv(g) returns the number of vertices.
ne(g) returns the number of edges (with multiple edges counted multiply).
edges(g) returns a list of the edges with multiple edges appearing repeatedly.
incidence_matrix(g) returns a signed incidence matrix of g. The i-th column of this matrix exactly corresponds to the i-th entry in the list returned by edges. Self loops render as all-zero columns.
SimpleGraph(g) returns a SimpleGraph (as defined in the Graphs module) by ignoring edge multiplicity in g.

Example

julia> g = EasyMultiGraph(5)
{5, 0} multigraph

julia> add!(g,1,2)
true

julia> add!(g,2,1)
true

julia> add!(g,3,3)
true

julia> add!(g,4,5)
true

julia> incidence_matrix(g)
5×4 Matrix{Int64}:
  1   1  0   0
 -1  -1  0   0
  0   0  0   0
  0   0  0   1
  0   0  0  -1

julia> edges(g)
4-element Vector{Tuple{Int64, Int64}}:
 (1, 2)
 (1, 2)
 (3, 3)
 (4, 5)

Why Create the `EasyMultiGraph` Type?

The Julia Graphs module does not allow multiple edges.