From d84c92c79315ca6c37dabc2090e09c9e6019a39c Mon Sep 17 00:00:00 2001
From: Inazuma110 <c011703534@edu.teu.ac.jp>
Date: Mon, 5 Oct 2020 17:43:57 +0900
Subject: [PATCH] fix conductance function and its test

---
 src/algorithms/conductance.jl | 13 +++++++------
 test/runtests.jl              | 14 +++++++-------
 2 files changed, 14 insertions(+), 13 deletions(-)

diff --git a/src/algorithms/conductance.jl b/src/algorithms/conductance.jl
index 8e49907..680849b 100644
--- a/src/algorithms/conductance.jl
+++ b/src/algorithms/conductance.jl
@@ -5,20 +5,21 @@ Calculate unweighted hypergraph conductance of `subset`.
 note: ∅ ⊊ `subset` ⊊ `1:nhv(h)`
 
 For more information see `1. Introduction` at:
-Generalizing the Hypergraph Laplacian via a Diffusion Processwith Mediators,
-auhtors: T-H. Hubert Chan, Xhibin Liang.
+Spectral Properties of Hypergraph Laplacian and Approximation Algorithms
+auhtors: T-H. Hubert Chan, Anand Louis, Zhihao Gavin Tang, and Chenzi Zhang
 """
 function conductance(h::Hypergraph, subset::Set{Int})::Float64
   if isempty(subset) error("`subset` is not allowed empty.") end
   if subset == Set(1:nhv(h)) error("`subset` is not allowed true subset of `h`.") end
   subset2 = setdiff(Set(1:nhv(h)), subset)
-  wₛ = sum([length(gethyperedges(h, node)) for node in subset])
-  w∂s = 0
+  volS = sum([sum(values(gethyperedges(h, node))) for node in subset])
+  volV_S = sum([sum(values(gethyperedges(h, node))) for node in subset2])
+  cutS = 0
   for he in 1:nhe(h)
     he_vertices = keys(getvertices(h, he))
     if isempty(intersect(he_vertices, subset)) continue end
     if isempty(intersect(he_vertices, subset2)) continue end
-    w∂s += length(getvertices(h, he))
+    cutS += 1
   end
-  return w∂s / wₛ
+  return cutS / min(volS, volV_S)
 end
diff --git a/test/runtests.jl b/test/runtests.jl
index d9c0e0a..7d83e2d 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -311,7 +311,7 @@ end;
     @test typeof(randompartition(hg, 2)) == Vector{Set{Int}}
     @test length(randompartition(hg, 2)) == 2
     @test sort(vcat(collect.(randompartition(hg, 2))...))==1:nhv(hg)
-    
+
     hh = Hypergraph{Bool}(7,4)
     hh[1,1] = true
     hh[2,1:2] .= true
@@ -474,10 +474,10 @@ end;
   h[4,3:4] .= 1
   h[5,4] = 1
   h[5,2] = 1
-  @test SimpleHypergraphs.conductance(h, Set(1:3)) == 5 / 5
-  @test SimpleHypergraphs.conductance(h, Set(1)) == 3 / 1
-  @test SimpleHypergraphs.conductance(h, Set([1, 4])) == 8 / 3
-  @test SimpleHypergraphs.conductance(h, Set(2:5)) == 3 / 8
+  @test SimpleHypergraphs.conductance(h, Set(1:3)) == 2 / 4
+  @test SimpleHypergraphs.conductance(h, Set(1)) == 1 / 1
+  @test SimpleHypergraphs.conductance(h, Set([1, 4])) == 3 / 3
+  @test SimpleHypergraphs.conductance(h, Set(2:5)) == SimpleHypergraphs.conductance(h, Set(1))
   h = Hypergraph{Int}(6, 7)
   h[1:3, 1] .= 1
   h[1:2, 2] .= 1
@@ -487,8 +487,8 @@ end;
   h[4:6, 5] .= 1
   h[4:5, 6] .= 1
   h[5:6, 7] .= 1
-  @test SimpleHypergraphs.conductance(h, Set(1:3)) == 2 / 8
-  @test SimpleHypergraphs.conductance(h, Set([1, 4])) == 14 / 6
+  @test SimpleHypergraphs.conductance(h, Set(1:3)) == 1 / 8
+  @test SimpleHypergraphs.conductance(h, Set([1, 4])) == 6 / 6
   @test_throws ErrorException SimpleHypergraphs.conductance(h, Set{Int}())
   @test_throws ErrorException SimpleHypergraphs.conductance(h, Set(1:nhv(h)))
 end;