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Add regular tree generator #197

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01896fe
add regular tree generator with test
Nov 23, 2022
dac8f9a
docstring for regular trees, one more test
Nov 23, 2022
7abb310
formatted according to JuliaFormatter
Nov 23, 2022
9a0fb29
fix error in docstring
Nov 23, 2022
f441197
add test for domain error
Nov 24, 2022
ec15727
new signature, InexactError, works for Int types
Nov 29, 2022
b26cf91
uniform signature style, fix overflow
Dec 19, 2022
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1 change: 1 addition & 0 deletions src/SimpleGraphs/SimpleGraphs.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -91,6 +91,7 @@ export AbstractSimpleGraph,
cycle_digraph,
binary_tree,
double_binary_tree,
regular_tree,
roach_graph,
clique_graph,
barbell_graph,
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48 changes: 48 additions & 0 deletions src/SimpleGraphs/generators/staticgraphs.jl
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Expand Up @@ -536,6 +536,54 @@ function double_binary_tree(k::Integer)
return g
end

"""
regular_tree(k::Integer, z::integer)

Create a [regular tree](https://en.wikipedia.org/wiki/Bethe_lattice),
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@simonschoelly simonschoelly Nov 24, 2022

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That wikipedia article might be a bit confusing, because it talks about infinite trees in the introduction.

Maybe we can decribe that a bit more clearly here?

If I understood correctly, what you want to create is a perfect k-ary tree such as described here? https://en.wikipedia.org/wiki/M-ary_tree#Types_of_m-ary_trees

also known as Bethe Lattice or Cayley Tree,
of depth `k` and degree `z`.

# Examples
```jldoctest
julia> regular_tree(4, 3)
{40, 39} undirected simple Int64 graph

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@aurorarossi aurorarossi Dec 7, 2022

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I would remove it and I would put it in the docstring of the function regular_tree(k,z).

Suggested change
julia> regular_tree(4, 3)
{40, 39} undirected simple Int64 graph

julia> regular_tree(5, 2) == binary_tree(5)
true
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@aurorarossi aurorarossi Dec 7, 2022

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Same as above.

Suggested change
julia> regular_tree(5, 2) == binary_tree(5)
true

```
"""
function regular_tree(k::T, z::T) where {T<:Integer}
k <= 0 && return SimpleGraph(0)
k == 1 && return SimpleGraph(1)
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@simonschoelly simonschoelly Nov 24, 2022

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In these cases we return a graph of of eltype Int, but in all other cases we return a graph of type T.

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@simonschoelly simonschoelly Nov 24, 2022

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To be completely honest, I am not sure if it is the best idea to determine the eltype of the graphs from k and z - we do that indeed for other graphs here, but I never really liked that.

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@simonschoelly simonschoelly Nov 24, 2022

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Maybe we can have a function signature

regular_tree(T::Type{<:Integer}, k::Integer, z::Integer)

and then define something like

regular_tree(k::Integer, z::Integer) = regular_tree(Int64, k, z)

that for be similar to the function sprand from SparseArrays for example.

if Graphs.isbounded(k) && BigInt(z)^k - 1 > typemax(k)
throw(DomainError(k, "z^k - 1 not representable by type $T"))
end

n = T((z^k - 1) / (z - 1))
ne = Int(n - 1)
fadjlist = Vector{Vector{T}}(undef, n)

@inbounds fadjlist[1] = convert.(T, 2:(z + 1))
@inbounds for l in 2:(k - 1)
w = Int((z^(l - 1) - 1) / (z - 1))
x = w + z^(l - 1)
@simd for i in 1:(z^(l - 1))
j = w + i
fadjlist[j] = [
ceil(T, (j - x) / z) + w
convert.(T, (x + (i - 1) * z + 1):(x + i * z))
]
end
end
l = k
w = Int((z^(l - 1) - 1) / (z - 1))
x = w + z^(l - 1)
@inbounds @simd for j in (w + 1):x
fadjlist[j] = T[ceil(Int, (j - x) / z) + w]
end
return SimpleGraph(ne, fadjlist)
end

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@aurorarossi aurorarossi Dec 7, 2022

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I would add the docstring also to this function.

Suggested change
"""
regular_tree(k, z)
Create a regular tree or [perfect z-ary tree](https://en.wikipedia.org/wiki/M-ary_tree#Types_of_m-ary_trees):
a `k`-level tree where all nodes except the leaves have exactly `z` children.
For `z = 2` one recovers a binary tree.
# Examples
```jldoctest
julia> regular_tree(4, 3)
{40, 39} undirected simple Int64 graph
julia> regular_tree(5, 2) == binary_tree(5)
true
```
"""

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@simonschoelly simonschoelly Dec 8, 2022

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It's quite often the case, that the docstrings for multiple methods of a function are only added for a single method - I think that would also be better here, than adding docstrings for both methods of this function.

"""
roach_graph(k)

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13 changes: 13 additions & 0 deletions test/simplegraphs/generators/staticgraphs.jl
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Expand Up @@ -411,6 +411,19 @@
@test isvalid_simplegraph(g)
end

@testset "Regular Trees" begin
g = @inferred(regular_tree(3, 3))
I = [1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]
J = [2, 3, 4, 1, 5, 6, 7, 8, 1, 9, 10, 1, 11, 12, 13, 2, 2, 2, 3, 3, 3, 4, 4, 4]
V = ones(Int, length(I))
Adj = sparse(I, J, V)
@test Adj == sparse(g)
@test isvalid_simplegraph(g)
@test_throws DomainError regular_tree(Int8(4), Int8(4))
# test that setting z = 2 recovers a binary tree
@test all(regular_tree(k, 2) == binary_tree(k) for k in 0:10)
end

@testset "Roach Graphs" begin
rg3 = @inferred(roach_graph(3))
# [3]
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