FunctionalBallDropping.DCHSBM_samplerMethod
DCHSBM_sampler(Z, θ, kmax)

Create a hypergraph sampler whose probability distribution follows the specified degree corrected hyperstochastic block model.

Draw a hypergraph from the sampler with rand(sampler).

Arguments

• Z::AbstractVector{<:Integer} the group assignment of each node
• θ::AbstractVector{<:Real} the degree correction weight of each node.
• kmax::Integer is the largest possible hyperedge size the graph will generate

Z and θ must have the same length.

Runtime

This method: O(tensor_cells * kmax + nodes) ≈ 400ns * tensor_cells * kmax + 30ns * nodes

Sampling: O(edges * kmax) ≈ 150ns * edges * kmax + 1300ns * edges

FunctionalBallDropping.Kronecker_samplerMethod
Kronecker_sampler(initializer, power; T=Int, space=1)

Create an efficient edge sampler whose probability distribution follows the specified kroneker model.

Giving the sampler an adequite (but not excessive) amount of space may speed up generation by up to 2x. space = edge_count ÷ 100 may be a good heuristic. The sampler will take up O(sizeof(t)*ndims(initailizer)*space) space with a constant factor around 4 bytes.

Draw a hypergraph from the sampler with rand(sampler, edges).

Base.randMethod
rand(s::DCHSBM_sampler[, edges::Integer])

Draw a hypergraph from the sampler s with edges edges

Base.randMethod
rand(s::Kronecker_sampler)
rand(s::Kronecker_sampler, e::Integer)

Draw an edge or a hypergraph with e edges from the sampler s.

FunctionalBallDropping.MEPSMethod
MEPS(;generators, size=100_000, trials=5)

Generate graphs of given size using each generator and report the number entries generated per second in millions (Millions of Entries Per Second)

The MEPS function is user facing and not part of the public API subject to symver.

FunctionalBallDropping.erMethod
er(n, m, k)

Sample a hypergraph with n nodes and m edges of edgesize ≤ k from an extension of the Erdős-Rényi graph model to hypergraphs.

Edges are drawn with replacement and weighted according to the number of ways they can be represented as a list of k nodes. For example, when k = 3 The edge joining nodes 1, 2, 3 has weight 6 with representations

[1, 2, 3]
[1, 3, 2]
[2, 1, 3]
[2, 3, 1]
[3, 1, 2]
[3, 2, 1]

The edge joining nodes 1 and 2 also has weight 6 with representations

[1, 1, 2]
[1, 2, 1]
[2, 1, 1]
[1, 2, 2]
[2, 1, 2]
[2, 2, 1]

While the edge containing only node 3 has weight 1 with the representation

[3, 3, 3]
FunctionalBallDropping.exampleFunction
example(Model, size)

generates an example graph using model Model with hypergraphsize of approximately size.

The example function is user facing and not part of the public API subject to symver.

Examples

example(DCHSBM_sampler, 100)

example(hyper_pa, 1_000_00)

example(Kronecker_sampler, 10)

example(Typing_sampler, 10_00)

example(er, 100_00)