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Added edge-betweenness.jl to centralities #277

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5 changes: 4 additions & 1 deletion src/Graphs.jl
Original file line number Diff line number Diff line change
Expand Up @@ -35,7 +35,8 @@ using Random:
seed!,
shuffle,
shuffle!
using SparseArrays: SparseMatrixCSC, nonzeros, nzrange, rowvals
using SparseArrays:
SparseMatrixCSC, nonzeros, nzrange, rowvals, spzeros, AbstractSparseMatrix
import SparseArrays: blockdiag, sparse
import Base:
adjoint,
Expand Down Expand Up @@ -250,6 +251,7 @@ export
desopo_pape_shortest_paths,

# centrality
edge_betweenness_centrality,
betweenness_centrality,
closeness_centrality,
degree_centrality,
Expand Down Expand Up @@ -504,6 +506,7 @@ include("operators.jl")
include("persistence/common.jl")
include("persistence/lg.jl")
include("centrality/betweenness.jl")
include("centrality/edge-betweenness.jl")
include("centrality/closeness.jl")
include("centrality/stress.jl")
include("centrality/degree.jl")
Expand Down
145 changes: 145 additions & 0 deletions src/centrality/edge-betweenness.jl
Original file line number Diff line number Diff line change
@@ -0,0 +1,145 @@
"""
edge_betweenness_centrality(g[, vertices, distmx]; [normalize])
edge_betweenness_centrality(g, k[, distmx]; [normalize, rng])

Compute the [edge betweenness centrality](https://en.wikipedia.org/wiki/Centrality#Betweenness_centrality)
of every edge `e` in a graph `g`. Or use a random subset of `k<|V|` vertices
to get an estimate of the edge betweenness centrality. Including more nodes yields better more accurate estimates.
Return a Sparse Matrix representing the centrality calculated for each edge in `g`.
It is defined as the sum of the fraction of all-pairs shortest paths that pass through `e`
``
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have you checked how this displays by building the docs?

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pkg> activate docs
julia> include("docs/make.jl")

bc(e) = \\sum_{s, t \\in V}
\\frac{\\sigma_{st}(e)}{\\sigma_{st}}
``.

where `V`, is the set of nodes, \\frac{\\sigma_{st}} is the number of shortest-paths, and \\frac{\\sigma_{st}(e)} is the number of those paths passing through edge.

### Optional Arguments
`normalize=true` : If set to true, the edge betweenness values will be normalized by the total number of possible distinct paths between all pairs of nodes in the graph.
For undirected graphs, the normalization factor is calculated as ``2 / (|V|(|V|-1))``, where |V| is the number of vertices. For directed graphs, the normalization factor
is calculated as ``1 / (|V|(|V|-1))``.
`vs=vertices(g)`: A subset of nodes in the graph g for which the edge betweenness centrality is to be estimated. By including more nodes in this subset,
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what is the relation between k and vs?

you can achieve a better estimate of the edge betweenness centrality.
`distmx=weights(g)`: The weights of the edges in the graph g represented as a matrix. This argument allows you to specify custom weights for the edges.
The weights can be used to influence the calculation of betweenness centrality, giving higher importance to certain edges over others.
`rng`: A random number generator used for selecting k vertices. This argument allows you to provide a custom random number generator that will be used for the vertex selection process.


### References
- Brandes 2001 & Brandes 2008
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can you give more details to help us check the algorithm?


# Examples
```jldoctest
julia> using Graphs

julia> Matrix(edge_betweenness_centrality(star_graph(5)))
5×5 Matrix{Float64}:
0.0 0.4 0.4 0.4 0.4
0.4 0.0 0.0 0.0 0.0
0.4 0.0 0.0 0.0 0.0
0.4 0.0 0.0 0.0 0.0
0.4 0.0 0.0 0.0 0.0

julia> Matrix(edge_betweenness_centrality(path_digraph(6), normalize=false))
6×6 Matrix{Float64}:
0.0 5.0 0.0 0.0 0.0 0.0
0.0 0.0 8.0 0.0 0.0 0.0
0.0 0.0 0.0 9.0 0.0 0.0
0.0 0.0 0.0 0.0 8.0 0.0
0.0 0.0 0.0 0.0 0.0 5.0
0.0 0.0 0.0 0.0 0.0 0.0

julia> g = SimpleGraph(Edge.([(1, 2), (2, 3), (2, 5), (3, 4), (4, 5), (5, 6)]));
julia> distmx = [
0.0 2.0 0.0 0.0 0.0 0.0
2.0 0.0 4.2 0.0 1.2 0.0
0.0 4.2 0.0 5.5 0.0 0.0
0.0 0.0 5.5 0.0 0.9 0.0
0.0 1.2 0.0 0.9 0.0 0.6
0.0 0.0 0.0 0.0 0.6 0.0
];

julia> Matrix(edge_betweenness_centrality(g; distmx=distmx, normalize=true))
6×6 Matrix{Float64}:
0.0 0.333333 … 0.0 0.0
0.333333 0.0 0.533333 0.0
0.0 0.266667 0.0 0.0
0.0 0.0 0.266667 0.0
0.0 0.533333 0.0 0.333333
0.0 0.0 … 0.333333 0.0
"""

function edge_betweenness_centrality(
g::AbstractGraph;
vs=vertices(g),
distmx::AbstractMatrix=weights(g),
normalize::Bool=true,
)
k = length(vs)
edge_betweenness = spzeros(nv(g), nv(g))
for source in vs
state = dijkstra_shortest_paths(
g, source, distmx; allpaths=true, trackvertices=true
)
_accumulate_edges!(edge_betweenness, state)
end
_rescale_e!(edge_betweenness, nv(g), normalize, is_directed(g), k)

return edge_betweenness
end

function edge_betweenness_centrality(
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g::AbstractGraph,
k::Integer;
distmx::AbstractMatrix=weights(g),
normalize=true,
rng::Union{Nothing,AbstractRNG}=nothing,
)
return edge_betweenness_centrality(
g;
vs=sample(collect_if_not_vector(vertices(g)), k; rng=rng),
distmx=distmx,
normalize=normalize,
)
end

function _accumulate_edges!(
edge_betweenness::AbstractSparseMatrix, state::Graphs.AbstractPathState
)
σ = state.pathcounts
pred = state.predecessors
seen = state.closest_vertices
δ = Dict(seen .=> 0.0)

while length(seen) > 0
w = pop!(seen)

coeff = (1.0 + δ[w]) / σ[w]
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can you explain the dynamics of coeff and δ through this loop?

for v in pred[w]
c = σ[v] * coeff
edge_betweenness[v, w] += c
δ[v] += c
end
end
return nothing
end

function _rescale_e!(
edge_betweenness::AbstractSparseMatrix,
n::Integer,
normalize::Bool,
directed::Bool,
k::Integer,
)
scale = n / k
if normalize
if n > 1
scale *= 1 / (n * (n - 1))
end
if !directed
scale *= 2
end
end
edge_betweenness .*= scale
return nothing
end
81 changes: 81 additions & 0 deletions test/centrality/edge-betweenness.jl
Original file line number Diff line number Diff line change
@@ -0,0 +1,81 @@

@testset "Edge Betweenness" begin
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how did you pick your test cases?

rng = StableRNG(1)
# self loops
s1 = GenericGraph(SimpleGraph(Edge.([(1, 2), (2, 3), (3, 3)])))
s2 = GenericDiGraph(SimpleDiGraph(Edge.([(1, 2), (2, 3), (3, 3)])))

g3 = GenericGraph(path_graph(5))

@test @inferred(edge_betweenness_centrality(s1)) ==
sparse([1, 2, 3, 2], [2, 1, 2, 3], [2 / 3, 2 / 3, 2 / 3, 2 / 3], 3, 3)
@test @inferred(edge_betweenness_centrality(s2)) ==
sparse([1, 2], [2, 3], [1 / 3, 1 / 3], 3, 3)

g = GenericGraph(path_graph(2))
z = @inferred(edge_betweenness_centrality(g; normalize=true))
@test z[1, 2] == z[2, 1] == 1.0
z2 = @inferred(edge_betweenness_centrality(g; vs=vertices(g)))
z3 = @inferred(edge_betweenness_centrality(g, nv(g)))
@test z == z2 == z3
z = @inferred(edge_betweenness_centrality(g3; normalize=false))
@test z[1, 2] == z[5, 4] == 4.0

##
# Weighted Graph tests
g = GenericGraph(SimpleGraph(Edge.([(1, 2), (2, 3), (2, 5), (3, 4), (4, 5), (5, 6)])))

distmx = [
0.0 2.0 0.0 0.0 0.0 0.0
2.0 0.0 4.2 0.0 1.2 0.0
0.0 4.2 0.0 5.5 0.0 0.0
0.0 0.0 5.5 0.0 0.9 0.0
0.0 1.2 0.0 0.9 0.0 0.6
0.0 0.0 0.0 0.0 0.6 0.0
]

@test isapprox(
nonzeros(
edge_betweenness_centrality(g; vs=vertices(g), distmx=distmx, normalize=false)
),
[5.0, 5.0, 4.0, 8.0, 4.0, 1.0, 1.0, 4.0, 8.0, 4.0, 5.0, 5.0],
)

@test isapprox(
nonzeros(
edge_betweenness_centrality(g; vs=vertices(g), distmx=distmx, normalize=true)
),
[5.0, 5.0, 4.0, 8.0, 4.0, 1.0, 1.0, 4.0, 8.0, 4.0, 5.0, 5.0] /
(nv(g) * (nv(g) - 1)) * 2,
)

adjmx2 = [0 1 0; 1 0 1; 1 1 0] # digraph
a2 = SimpleDiGraph(adjmx2)

for g in test_generic_graphs(a2)
distmx2 = [Inf 2.0 Inf; 3.2 Inf 4.2; 5.5 6.1 Inf]
c2 = [0.24390243902439027, 0.27027027027027023, 0.1724137931034483]

@test isapprox(
nonzeros(
edge_betweenness_centrality(
g; vs=vertices(g), distmx=distmx2, normalize=false
),
),
[1.0, 1.0, 2.0, 1.0, 2.0],
)

@test isapprox(
nonzeros(
edge_betweenness_centrality(
g; vs=vertices(g), distmx=distmx2, normalize=true
),
),
[1.0, 1.0, 2.0, 1.0, 2.0] * (1 / 6),
)
end
# test #1405 / #1406
g = GenericGraph(grid([50, 50]))
z = edge_betweenness_centrality(g; normalize=false)
@test maximum(z) < nv(g) * (nv(g) - 1)
end
14 changes: 10 additions & 4 deletions test/runtests.jl
Original file line number Diff line number Diff line change
Expand Up @@ -31,7 +31,9 @@ end
@testset "Code quality (JET.jl)" begin
if VERSION >= v"1.9"
@assert get_pkg_version("JET") >= v"0.8.4"
JET.test_package(Graphs; target_defined_modules=true, ignore_missing_comparison=true)
JET.test_package(
Graphs; target_defined_modules=true, ignore_missing_comparison=true
)
end
end

Expand Down Expand Up @@ -70,7 +72,7 @@ function test_generic_graphs(g; eltypes=[UInt8, Int16], skip_if_too_large::Bool=
SG = is_directed(g) ? SimpleDiGraph : SimpleGraph
GG = is_directed(g) ? GenericDiGraph : GenericGraph
result = GG[]
for T in eltypes
for T in eltypes
if skip_if_too_large && nv(g) > typemax(T)
continue
end
Expand All @@ -79,8 +81,11 @@ function test_generic_graphs(g; eltypes=[UInt8, Int16], skip_if_too_large::Bool=
return result
end

test_large_generic_graphs(g; skip_if_too_large::Bool=false) = test_generic_graphs(g; eltypes=[UInt16, Int32], skip_if_too_large=skip_if_too_large)

function test_large_generic_graphs(g; skip_if_too_large::Bool=false)
return test_generic_graphs(
g; eltypes=[UInt16, Int32], skip_if_too_large=skip_if_too_large
)
end

tests = [
"simplegraphs/runtests",
Expand Down Expand Up @@ -124,6 +129,7 @@ tests = [
"community/clique_percolation",
"community/assortativity",
"community/rich_club",
"centrality/edge-betweenness",
"centrality/betweenness",
"centrality/closeness",
"centrality/degree",
Expand Down