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Add regular tree generator #197

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1 change: 1 addition & 0 deletions src/SimpleGraphs/SimpleGraphs.jl
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
Original file line number Diff line number Diff line change
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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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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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
Comment on lines +554 to +556
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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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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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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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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"))
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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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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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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
Original file line number Diff line number Diff line change
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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