Graph Types

When creating Graphon objects, we can specify the type of graph to be sampled. By default, the sampled graphs are dense matrices. However, we can specify SparseMatrixCSC to obtain sparse graphs (should be supported by default), but other types are also possible.

Work in Progress

This section is a work in progress. More graph types will be added in the future.

Design Philosophy

One of the main difficulties is that we cannot know what value is used to represent a non-edge in a decorated graph type. For example, for a simple graph encoded in a BitMatrix, a non-edge is represented by false. But for a weighted graph encoded in a Matrix{Float64}, there is no necessarily a default value for a non-edge. It could be 0.0, NaN, or any other value.

To circumvent this issue, we have decided to let the user define how to create an empty graph of a given type if the default is not suitable. This means that the function to randomly sample a graph with preallocated memory now expects that the input graph is empty and of the right size.

Graphons._rand! — Function

_rand!(rng::AbstractRNG, f::AbstractGraphon{T,M}, A::M, ξs)

Generates a random graph according to the graphon `f` and the latent positions `ξs`.
The generated graph is stored in `A`.

Warning

This function expects that A is an empty graph of the right size and type. It does not try to clean it up before filling it. See make_empty_graph for more details.

source

Custom Graph Types

To sample with your own graph type, you need to redefine the function make_empty_graph(::Type{M}, n), such that it returns an empty graph of type M with n nodes and no edges.

Design Choice

Since for decorated graphs it is sometimes hard to know in advance what will be the default representation of a non-edge, we have left that choice to the user via the make_empty_graph function.

An example of a custom graph type is provided in ext/SuiteSparseGraphBLAS.jl, which uses the SuiteSparseGraphBLAS package to create large sparse graphs efficiently.

function make_empty_graph(::Type{GB}, n) where {GB<:GBMatrix}
    return GB(n, n)
end

This allows us to create a Graphon object that will sample graphs of type GBMatrix:

using SuiteSparseGraphBLAS
f_sparseBLAS = SimpleContinuousGraphon((x,y)-> 0.1, GBMatrix{Bool})
A = rand(f_sparseBLAS, 41)

Custom Distribution Types

For information on implementing custom distribution types to use with DecoratedGraphon, see the Custom Distribution Types page.