From bffb5a6c064c49a87f83435368a4f8f891b4e46e Mon Sep 17 00:00:00 2001
From: Yuren Hao <blackhao0426@gmail.com>
Date: Tue, 24 Feb 2026 08:53:02 +0000
Subject: Add edge connectivity analysis, use official network_evaluation
 scripts

- Switch accuracy computation to official network_evaluation scripts
  (clustering_accuracy with graph-tool NMI/AMI and sklearn ARI)
- Add minimum edge cut / log10(n) and well-connectedness stats
- Add edge connectivity boxplots and well-connected fraction bar chart
- Add "What I Learned and Open Questions" section to discussion
- Fix author name and minor LaTeX issues
---
 .../polblogs/leiden_cpm_01/cluster_details.json    | 580 +++++++++++++++------
 1 file changed, 435 insertions(+), 145 deletions(-)

(limited to 'results/stats/polblogs/leiden_cpm_01/cluster_details.json')

diff --git a/results/stats/polblogs/leiden_cpm_01/cluster_details.json b/results/stats/polblogs/leiden_cpm_01/cluster_details.json
index 21d6e46..a0d4be0 100644
--- a/results/stats/polblogs/leiden_cpm_01/cluster_details.json
+++ b/results/stats/polblogs/leiden_cpm_01/cluster_details.json
@@ -6,7 +6,9 @@
     "c_boundary": 3978,
     "edge_density": 0.26114501598372564,
     "degree_density": 24.155913978494624,
-    "conductance": 0.3068497377352669
+    "conductance": 0.3068497377352669,
+    "mincut": 19,
+    "mincut_over_log10n": 8.371840331823918
   },
   {
     "com_id": "1",
@@ -15,7 +17,9 @@
     "c_boundary": 5082,
     "edge_density": 0.2265193370165746,
     "degree_density": 20.5,
-    "conductance": 0.40513392857142855
+    "conductance": 0.40513392857142855,
+    "mincut": 19,
+    "mincut_over_log10n": 8.406814094903039
   },
   {
     "com_id": "10",
@@ -24,7 +28,9 @@
     "c_boundary": 68,
     "edge_density": 0.2857142857142857,
     "degree_density": 1.0,
-    "conductance": 0.8095238095238095
+    "conductance": 0.8095238095238095,
+    "mincut": 1,
+    "mincut_over_log10n": 1.1073093649624541
   },
   {
     "com_id": "100",
@@ -33,7 +39,9 @@
     "c_boundary": 4,
     "edge_density": 0.6666666666666666,
     "degree_density": 0.6666666666666666,
-    "conductance": 0.5
+    "conductance": 0.5,
+    "mincut": 1,
+    "mincut_over_log10n": 2.095903274289385
   },
   {
     "com_id": "101",
@@ -42,7 +50,9 @@
     "c_boundary": 22,
     "edge_density": 0.6666666666666666,
     "degree_density": 0.6666666666666666,
-    "conductance": 0.8461538461538461
+    "conductance": 0.8461538461538461,
+    "mincut": 1,
+    "mincut_over_log10n": 2.095903274289385
   },
   {
     "com_id": "102",
@@ -51,7 +61,9 @@
     "c_boundary": 50,
     "edge_density": 0.6666666666666666,
     "degree_density": 0.6666666666666666,
-    "conductance": 0.9259259259259259
+    "conductance": 0.9259259259259259,
+    "mincut": 1,
+    "mincut_over_log10n": 2.095903274289385
   },
   {
     "com_id": "103",
@@ -60,7 +72,9 @@
     "c_boundary": 12,
     "edge_density": 0.6666666666666666,
     "degree_density": 0.6666666666666666,
-    "conductance": 0.75
+    "conductance": 0.75,
+    "mincut": 1,
+    "mincut_over_log10n": 2.095903274289385
   },
   {
     "com_id": "104",
@@ -69,7 +83,9 @@
     "c_boundary": 3,
     "edge_density": 0.6666666666666666,
     "degree_density": 0.6666666666666666,
-    "conductance": 0.42857142857142855
+    "conductance": 0.42857142857142855,
+    "mincut": 1,
+    "mincut_over_log10n": 2.095903274289385
   },
   {
     "com_id": "105",
@@ -78,7 +94,9 @@
     "c_boundary": 18,
     "edge_density": 0.6666666666666666,
     "degree_density": 0.6666666666666666,
-    "conductance": 0.8181818181818182
+    "conductance": 0.8181818181818182,
+    "mincut": 1,
+    "mincut_over_log10n": 2.095903274289385
   },
   {
     "com_id": "106",
@@ -87,7 +105,9 @@
     "c_boundary": 14,
     "edge_density": 0.6666666666666666,
     "degree_density": 0.6666666666666666,
-    "conductance": 0.7777777777777778
+    "conductance": 0.7777777777777778,
+    "mincut": 1,
+    "mincut_over_log10n": 2.095903274289385
   },
   {
     "com_id": "107",
@@ -96,7 +116,9 @@
     "c_boundary": 29,
     "edge_density": 0.6666666666666666,
     "degree_density": 0.6666666666666666,
-    "conductance": 0.8787878787878788
+    "conductance": 0.8787878787878788,
+    "mincut": 1,
+    "mincut_over_log10n": 2.095903274289385
   },
   {
     "com_id": "108",
@@ -105,7 +127,9 @@
     "c_boundary": 24,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.9230769230769231
+    "conductance": 0.9230769230769231,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "109",
@@ -114,7 +138,9 @@
     "c_boundary": 10,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.8333333333333334
+    "conductance": 0.8333333333333334,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "11",
@@ -123,7 +149,9 @@
     "c_boundary": 98,
     "edge_density": 0.2857142857142857,
     "degree_density": 1.0,
-    "conductance": 0.8596491228070176
+    "conductance": 0.8596491228070176,
+    "mincut": 1,
+    "mincut_over_log10n": 1.1073093649624541
   },
   {
     "com_id": "110",
@@ -132,7 +160,9 @@
     "c_boundary": 13,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.8666666666666667
+    "conductance": 0.8666666666666667,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "111",
@@ -141,7 +171,9 @@
     "c_boundary": 10,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.8333333333333334
+    "conductance": 0.8333333333333334,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "112",
@@ -150,7 +182,9 @@
     "c_boundary": 17,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.8947368421052632
+    "conductance": 0.8947368421052632,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "113",
@@ -159,7 +193,9 @@
     "c_boundary": 18,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.9
+    "conductance": 0.9,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "114",
@@ -168,7 +204,9 @@
     "c_boundary": 27,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.9310344827586207
+    "conductance": 0.9310344827586207,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "115",
@@ -177,7 +215,9 @@
     "c_boundary": 24,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.9230769230769231
+    "conductance": 0.9230769230769231,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "116",
@@ -186,7 +226,9 @@
     "c_boundary": 4,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.6666666666666666
+    "conductance": 0.6666666666666666,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "117",
@@ -195,7 +237,9 @@
     "c_boundary": 16,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.8888888888888888
+    "conductance": 0.8888888888888888,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "118",
@@ -204,7 +248,9 @@
     "c_boundary": 10,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.8333333333333334
+    "conductance": 0.8333333333333334,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "119",
@@ -213,7 +259,9 @@
     "c_boundary": 19,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.9047619047619048
+    "conductance": 0.9047619047619048,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "12",
@@ -222,7 +270,9 @@
     "c_boundary": 75,
     "edge_density": 0.39285714285714285,
     "degree_density": 1.375,
-    "conductance": 0.7731958762886598
+    "conductance": 0.7731958762886598,
+    "mincut": 1,
+    "mincut_over_log10n": 1.1073093649624541
   },
   {
     "com_id": "120",
@@ -231,7 +281,9 @@
     "c_boundary": 19,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.9047619047619048
+    "conductance": 0.9047619047619048,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "121",
@@ -240,7 +292,9 @@
     "c_boundary": 12,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.8571428571428571
+    "conductance": 0.8571428571428571,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "122",
@@ -249,7 +303,9 @@
     "c_boundary": 13,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.8666666666666667
+    "conductance": 0.8666666666666667,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "123",
@@ -258,7 +314,9 @@
     "c_boundary": 6,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.75
+    "conductance": 0.75,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "124",
@@ -267,7 +325,9 @@
     "c_boundary": 7,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.7777777777777778
+    "conductance": 0.7777777777777778,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "125",
@@ -276,7 +336,9 @@
     "c_boundary": 6,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.75
+    "conductance": 0.75,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "126",
@@ -285,7 +347,9 @@
     "c_boundary": 6,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.75
+    "conductance": 0.75,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "127",
@@ -294,7 +358,9 @@
     "c_boundary": 4,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.6666666666666666
+    "conductance": 0.6666666666666666,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "128",
@@ -303,7 +369,9 @@
     "c_boundary": 5,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.7142857142857143
+    "conductance": 0.7142857142857143,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "129",
@@ -312,7 +380,9 @@
     "c_boundary": 4,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.6666666666666666
+    "conductance": 0.6666666666666666,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "13",
@@ -321,7 +391,9 @@
     "c_boundary": 94,
     "edge_density": 0.25,
     "degree_density": 0.875,
-    "conductance": 0.8703703703703703
+    "conductance": 0.8703703703703703,
+    "mincut": 1,
+    "mincut_over_log10n": 1.1073093649624541
   },
   {
     "com_id": "130",
@@ -330,7 +402,9 @@
     "c_boundary": 3,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.6
+    "conductance": 0.6,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "131",
@@ -339,7 +413,9 @@
     "c_boundary": 2,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.5
+    "conductance": 0.5,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "132",
@@ -348,7 +424,9 @@
     "c_boundary": 2,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.5
+    "conductance": 0.5,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "133",
@@ -357,7 +435,9 @@
     "c_boundary": 1,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.3333333333333333
+    "conductance": 0.3333333333333333,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "134",
@@ -366,7 +446,9 @@
     "c_boundary": 22,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.9166666666666666
+    "conductance": 0.9166666666666666,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "135",
@@ -375,7 +457,9 @@
     "c_boundary": 10,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.8333333333333334
+    "conductance": 0.8333333333333334,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "136",
@@ -384,7 +468,9 @@
     "c_boundary": 6,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.75
+    "conductance": 0.75,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "137",
@@ -393,7 +479,9 @@
     "c_boundary": 2,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.5
+    "conductance": 0.5,
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+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "138",
@@ -402,7 +490,9 @@
     "c_boundary": 18,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.9
+    "conductance": 0.9,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "139",
@@ -411,7 +501,9 @@
     "c_boundary": 3,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.6
+    "conductance": 0.6,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "14",
@@ -420,7 +512,9 @@
     "c_boundary": 77,
     "edge_density": 0.25,
     "degree_density": 0.875,
-    "conductance": 0.8461538461538461
+    "conductance": 0.8461538461538461,
+    "mincut": 1,
+    "mincut_over_log10n": 1.1073093649624541
   },
   {
     "com_id": "140",
@@ -429,7 +523,9 @@
     "c_boundary": 11,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.8461538461538461
+    "conductance": 0.8461538461538461,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "141",
@@ -438,7 +534,9 @@
     "c_boundary": 5,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.7142857142857143
+    "conductance": 0.7142857142857143,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "142",
@@ -447,7 +545,9 @@
     "c_boundary": 1,
     "edge_density": 1.0,
     "degree_density": 0.5,
-    "conductance": 0.3333333333333333
+    "conductance": 0.3333333333333333,
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   },
   {
     "com_id": "143",
@@ -456,7 +556,9 @@
     "c_boundary": 0,
     "edge_density": 1.0,
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   },
   {
     "com_id": "144",
@@ -465,7 +567,9 @@
     "c_boundary": 13,
     "edge_density": 1.0,
     "degree_density": 0.5,
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+    "conductance": 0.8666666666666667,
+    "mincut": 1,
+    "mincut_over_log10n": 3.321928094887362
   },
   {
     "com_id": "15",
@@ -474,7 +578,9 @@
     "c_boundary": 109,
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     "degree_density": 1.0,
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+    "conductance": 0.8861788617886179,
+    "mincut": 1,
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   },
   {
     "com_id": "16",
@@ -483,7 +589,9 @@
     "c_boundary": 51,
     "edge_density": 0.2857142857142857,
     "degree_density": 0.8571428571428571,
-    "conductance": 0.8095238095238095
+    "conductance": 0.8095238095238095,
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+    "mincut_over_log10n": 1.1832946624549383
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   {
     "com_id": "17",
@@ -492,7 +600,9 @@
     "c_boundary": 55,
     "edge_density": 0.2857142857142857,
     "degree_density": 0.8571428571428571,
-    "conductance": 0.8208955223880597
+    "conductance": 0.8208955223880597,
+    "mincut": 1,
+    "mincut_over_log10n": 1.1832946624549383
   },
   {
     "com_id": "18",
@@ -501,7 +611,9 @@
     "c_boundary": 52,
     "edge_density": 0.2857142857142857,
     "degree_density": 0.8571428571428571,
-    "conductance": 0.8125
+    "conductance": 0.8125,
+    "mincut": 1,
+    "mincut_over_log10n": 1.1832946624549383
   },
   {
     "com_id": "19",
@@ -510,7 +622,9 @@
     "c_boundary": 76,
     "edge_density": 0.4,
     "degree_density": 1.0,
-    "conductance": 0.8636363636363636
+    "conductance": 0.8636363636363636,
+    "mincut": 1,
+    "mincut_over_log10n": 1.2850972089384687
   },
   {
     "com_id": "2",
@@ -519,7 +633,9 @@
     "c_boundary": 263,
     "edge_density": 0.34065934065934067,
     "degree_density": 2.2142857142857144,
-    "conductance": 0.8092307692307692
+    "conductance": 0.8092307692307692,
+    "mincut": 2,
+    "mincut_over_log10n": 1.7450057390983118
   },
   {
     "com_id": "20",
@@ -528,7 +644,9 @@
     "c_boundary": 58,
     "edge_density": 0.3333333333333333,
     "degree_density": 0.8333333333333334,
-    "conductance": 0.8529411764705882
+    "conductance": 0.8529411764705882,
+    "mincut": 1,
+    "mincut_over_log10n": 1.2850972089384687
   },
   {
     "com_id": "21",
@@ -537,7 +655,9 @@
     "c_boundary": 83,
     "edge_density": 0.4,
     "degree_density": 1.0,
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@@ -1095,7 +1337,9 @@
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+    "conductance": 0.9325842696629213,
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@@ -1104,7 +1348,9 @@
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+    "conductance": 0.8604651162790697,
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@@ -1113,7 +1359,9 @@
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     "degree_density": 0.8888888888888888,
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+    "conductance": 0.7647058823529411,
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@@ -1122,7 +1370,9 @@
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+    "conductance": 0.8695652173913043,
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@@ -1131,7 +1381,9 @@
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+    "conductance": 0.8823529411764706,
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@@ -1140,7 +1392,9 @@
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     "degree_density": 0.75,
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+    "conductance": 0.8846153846153846,
+    "mincut": 1,
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@@ -1149,7 +1403,9 @@
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     "degree_density": 0.75,
-    "conductance": 0.8695652173913043
+    "conductance": 0.8695652173913043,
+    "mincut": 1,
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@@ -1158,7 +1414,9 @@
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     "edge_density": 0.5,
     "degree_density": 0.75,
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+    "conductance": 0.85,
+    "mincut": 1,
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@@ -1167,7 +1425,9 @@
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     "degree_density": 0.75,
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+    "conductance": 0.8421052631578947,
+    "mincut": 1,
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@@ -1176,7 +1436,9 @@
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     "edge_density": 0.5,
     "degree_density": 0.75,
-    "conductance": 0.7857142857142857
+    "conductance": 0.7857142857142857,
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@@ -1185,7 +1447,9 @@
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     "edge_density": 0.5,
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+    "conductance": 0.9154929577464789,
+    "mincut": 1,
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@@ -1194,7 +1458,9 @@
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     "degree_density": 0.75,
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@@ -1203,7 +1469,9 @@
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+    "conductance": 0.8723404255319149,
+    "mincut": 1,
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@@ -1212,7 +1480,9 @@
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     "degree_density": 0.8888888888888888,
-    "conductance": 0.8504672897196262
+    "conductance": 0.8504672897196262,
+    "mincut": 1,
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@@ -1221,7 +1491,9 @@
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     "degree_density": 0.6666666666666666,
-    "conductance": 0.8461538461538461
+    "conductance": 0.8461538461538461,
+    "mincut": 1,
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@@ -1230,7 +1502,9 @@
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     "degree_density": 0.6666666666666666,
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+    "conductance": 0.8823529411764706,
+    "mincut": 1,
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@@ -1239,7 +1513,9 @@
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     "degree_density": 0.6666666666666666,
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+    "conductance": 0.8947368421052632,
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@@ -1248,7 +1524,9 @@
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     "degree_density": 0.6666666666666666,
-    "conductance": 0.84
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@@ -1257,7 +1535,9 @@
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     "degree_density": 0.6666666666666666,
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+    "conductance": 0.8947368421052632,
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@@ -1266,7 +1546,9 @@
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     "degree_density": 0.6666666666666666,
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@@ -1275,7 +1557,9 @@
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     "degree_density": 0.6666666666666666,
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+    "conductance": 0.8709677419354839,
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@@ -1284,7 +1568,9 @@
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     "degree_density": 0.6666666666666666,
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@@ -1293,7 +1579,9 @@
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     "degree_density": 0.6666666666666666,
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+    "conductance": 0.8095238095238095,
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@@ -1302,6 +1590,8 @@
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     "degree_density": 0.6666666666666666,
-    "conductance": 0.9148936170212766
+    "conductance": 0.9148936170212766,
+    "mincut": 1,
+    "mincut_over_log10n": 2.095903274289385
   }
 ]
\ No newline at end of file
-- 
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