Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Jump to bottom

Add regular tree generator #197

Open
wants to merge 7 commits into
base: master
Choose a base branch
from
Open

Add regular tree generator #197

Show file tree
Hide file tree
Changes from 5 commits
Commits
Show all changes
7 commits
Select commit Hold shift + click to select a range
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
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
1 change: 1 addition & 0 deletions src/SimpleGraphs/SimpleGraphs.jl
View file
Open in desktop
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,
Expand Down
48 changes: 48 additions & 0 deletions src/SimpleGraphs/generators/staticgraphs.jl
View file
Open in desktop
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),
Copy link
Contributor

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

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

Comment on lines +549 to +551
Copy link
Member

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

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
Copy link
Member

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

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)
Copy link
Contributor

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

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

Copy link
Contributor

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

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.

Copy link
Contributor

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

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"))
aurorarossi marked this conversation as resolved.
Show resolved Hide resolved
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

Copy link
Member

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

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
```
"""

Copy link
Contributor

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

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)

Expand Down
13 changes: 13 additions & 0 deletions test/simplegraphs/generators/staticgraphs.jl
View file
Open in desktop
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]
Expand Down