Louvain method

[afternone]

Here is an efficient implementation of the Louvain fast-unfolding algorithm based on PR #3 . It calculates the modularity change directly and fixes some problems of the implementation in #3. The comparison shows that its performance is very good. Please feel free to comment or make changes.

julia> g = CliqueGraph(10, 100)
{1000, 4600} undirected simple Int64 graph

julia> @benchmark c = community_detection_louvain_old(g)
BenchmarkTools.Trial: 11 samples with 1 evaluation.
 Range (min … max):  475.899 ms … 493.400 ms  ┊ GC (min … max): 3.34% … 3.14%
 Time  (median):     478.429 ms               ┊ GC (median):    3.41%
 Time  (mean ± σ):   480.148 ms ±   5.228 ms  ┊ GC (mean ± σ):  3.40% ± 0.13%

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  493 ms           Histogram: frequency by time          486 ms <

 Memory estimate: 1.47 GiB, allocs estimate: 8927625.

julia> @benchmark c = community_detection_louvain(g)
BenchmarkTools.Trial: 4721 samples with 1 evaluation.
 Range (min … max):  721.900 μs …   3.174 ms  ┊ GC (min … max): 0.00% … 64.60%
 Time  (median):       1.018 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):     1.055 ms ± 255.500 μs  ┊ GC (mean ± σ):  3.90% ±  9.54%

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  1.21 ms          Histogram: frequency by time          859 μs <

 Memory estimate: 1.28 MiB, allocs estimate: 4788.
 
 
 julia> g = CliqueGraph(5,8)
{40, 88} undirected simple Int64 graph

julia> c = community_detection_louvain_old(g)'
1×40 adjoint(::Vector{Int64}) with eltype Int64:
 1  1  1  1  1  1  1  1  1  1  2  2  2  2  2  2  2  2  2  2  3  3  3  3  3  3  3  3  3  3  4  4  4  4  4  4  4  4  4  4

julia> c = community_detection_louvain(g)'
1×40 adjoint(::Vector{Int64}) with eltype Int64:
 1  1  1  1  1  2  2  2  2  2  3  3  3  3  3  4  4  4  4  4  5  5  5  5  5  6  6  6  6  6  7  7  7  7  7  8  8  8  8  8     

[storopoli]

This is great I hope this gets merged soon!

We could tackle Leiden afterwards. There is an old implementation in bicycle1885 /Leiden.jl that is MIT licensed.

[storopoli]

Now that CommunityDetection.jl is being somewhat maintained we can take a look at this.

@matbesancon do you want me to review this PR? You can assign me as a reviewer if you want.

@afternone do you think something should be updated in the PR? I can deal with the LighGraphs -> Graphs migration for you. What I mean is "do you think any Julia 1.6 feature might be incorporated or updated in this PR?"

[elisno]

I hope we can add a resolution parameter (γ=1.0) like the one Graphs.modularity accepts.

AFAICT, it should be sufficient to scale the updates to node_comm_W[neighbor_comm] by this resolution.

EDIT: Maybe comm_W[...] as well?

[matbesancon]

yes that would be great, after the conflict has been resolved

[gdalle]

@afternone sorry for the huge delay, this repo is barely active as you can see. Can I suggest you submit the same PR to Graphs.jl?

[gdalle]

Without the SimpleWeightedGraphs dependency of course

[gdalle]

@matbesancon can you think of a way to remove the dependency on Clustering in order to add this code to the main repo?