Custom Value Graph types

While this package provides some concrete graph types, one is often interested in creating their own graph types. This section will explain how one can create a custom graph type that will work well with the methods from as package as well as the ones from Graphs.jl

The AbstractValGraph type

All value graphs should be subtypes of AbstractValGraph that has the signature

    AbstractValGraph{V <: Integer, V_VALS, E_VALS, G_VALS} <: Graphs.AbstractGraph{V}

where the parameters have the following meaning:

V is the type used for indexing vertices, called the eltype of the graph. Should be a subtype of Integer.
V_VALS is the type of the vertex values.
E_VALS is the type of the edge values.
G_VALS is the type of the graph values.

The value types V_VALS, E_VALS and G_VALS are either subtypes of Tuple for unnamed values or of NamedTuple for named values.

A subtype of AbstractValGraph is free to restrict some of these parameters, for example

MyGraphType{W} <: AbstractValGraph{Int, Tuple{}, Tuple{Int, W}, Tuple{}}

is a graph type that has neither vertex nor graph values and two edge values, one of them of type Int and the other of type W.

As a subtype of Graphs.AbstractGraph, an AbstractValGraph should implement the methods required by Graphs.jl as well as some other methods. Luckily a lot of the methods required for AbstractGraph already have a default implementation, so the number of necessary methods is actually much shorter.

We distinguish between methods that need to be implemented, methods that only need to be implemented in some cases to enable extra features, and methods that have a default implementation that can be overridden for performance or other reasons.

Necessary methods

method	brief description
`nv(g)`	number of vertices
`has_edge(g, s, d)`	true if there is an edge from vertex `s` to `d`
`is_directed(G)`	true if graph type `G` is directed
`zero(G)`	create an instance of graph type `G` without vertices

Necessary in some cases

method	necessary if	brief description
`get_graphval(g, i)`	`g` has graph values	i-th graph value of `g`
`get_vertexval(g, v, i)`	`g` has vertex values	i-th vertex value of vertex `v`
`get_edgevalval(g, s, d, i)`	`g` has edge values	i-th edge value of the edge `s -> d`

`set_graphval!(g, i, val)`	one can set graph values	set the i-th graph value of `g`
`set_vertexval!(g, v, i, val)`	one can set vertex values	set the i-th vertex value of vertex `v`
`set_edgevalval!(g, s, d, i, val)`	one can set edge values	set the i-th edge value of the edge `s -> d`

`add_vertex!(g, vals)`	one can add vertices	add a vertex with values `vals`
`rem_vertex!(g, v)`	one can remove vertices	remove vertex `v`

`add_edge!(g, s, d, vals)`	one can add edges	add an edge `s -> d` with values `vals`
`rem_edge!(g, s, d)`	one can remove edges	remove the edge `s -> d`

Methods with default implementations

method	brief description
`ne(g)`	number of edges

TODO there are more

Changing the edgetype

TODO