Add edge connectivity analysis, use official network_evaluation scriptsHEADmaster

- 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

1 files changed, 150 insertions, 50 deletions

diff --git a/results/stats/topology/leiden_mod/cluster_details.json b/results/stats/topology/leiden_mod/cluster_details.json
index dc14eb7..fd9ef45 100644
--- a/results/stats/topology/leiden_mod/cluster_details.json
+++ b/results/stats/topology/leiden_mod/cluster_details.json
@@ -6,7 +6,9 @@
     "c_boundary": 7909,
     "edge_density": 0.0003318949570026178,
     "degree_density": 1.797045244690674,
-    "conductance": 0.1688766468088741
+    "conductance": 0.1688766468088741,
+    "mincut": 1,
+    "mincut_over_log10n": 0.24785429705624712
   },
   {
     "com_id": "1",
@@ -15,7 +17,9 @@
     "c_boundary": 18718,
     "edge_density": 0.004006421550591582,
     "degree_density": 7.037279453614115,
-    "conductance": 0.27455409528279745
+    "conductance": 0.27455409528279745,
+    "mincut": 1,
+    "mincut_over_log10n": 0.2820236630491016
   },
   {
     "com_id": "10",
@@ -24,7 +28,9 @@
     "c_boundary": 614,
     "edge_density": 0.0050454603662440775,
     "degree_density": 1.7255474452554744,
-    "conductance": 0.20617864338482203
+    "conductance": 0.20617864338482203,
+    "mincut": 1,
+    "mincut_over_log10n": 0.35264778535892916
   },
   {
     "com_id": "11",
@@ -33,7 +39,9 @@
     "c_boundary": 494,
     "edge_density": 0.00497114131446658,
     "degree_density": 1.6280487804878048,
-    "conductance": 0.18783269961977186
+    "conductance": 0.18783269961977186,
+    "mincut": 1,
+    "mincut_over_log10n": 0.35499969364294676
   },
   {
     "com_id": "12",
@@ -42,7 +50,9 @@
     "c_boundary": 1016,
     "edge_density": 0.007181118911739378,
     "degree_density": 1.8778625954198473,
-    "conductance": 0.34048257372654156
+    "conductance": 0.34048257372654156,
+    "mincut": 1,
+    "mincut_over_log10n": 0.3677374672172425
   },
   {
     "com_id": "13",
@@ -51,7 +61,9 @@
     "c_boundary": 315,
     "edge_density": 0.006026685420695853,
     "degree_density": 1.3620309050772628,
-    "conductance": 0.20335700451904454
+    "conductance": 0.20335700451904454,
+    "mincut": 1,
+    "mincut_over_log10n": 0.37649210380933384
   },
   {
     "com_id": "14",
@@ -60,7 +72,9 @@
     "c_boundary": 489,
     "edge_density": 0.007689036921550563,
     "degree_density": 1.5800970873786409,
-    "conductance": 0.2730318257956449
+    "conductance": 0.2730318257956449,
+    "mincut": 1,
+    "mincut_over_log10n": 0.38242420920736053
   },
   {
     "com_id": "15",
@@ -69,7 +83,9 @@
     "c_boundary": 664,
     "edge_density": 0.006972618205729458,
     "degree_density": 1.3980099502487562,
-    "conductance": 0.3713646532438479
+    "conductance": 0.3713646532438479,
+    "mincut": 1,
+    "mincut_over_log10n": 0.3839912433160672
   },
   {
     "com_id": "16",
@@ -78,7 +94,9 @@
     "c_boundary": 248,
     "edge_density": 0.008648825065274151,
     "degree_density": 1.65625,
-    "conductance": 0.1631578947368421
+    "conductance": 0.1631578947368421,
+    "mincut": 1,
+    "mincut_over_log10n": 0.38694730403403776
   },
   {
     "com_id": "17",
@@ -87,7 +105,9 @@
     "c_boundary": 348,
     "edge_density": 0.008427807486631016,
     "degree_density": 1.576,
-    "conductance": 0.22745098039215686
+    "conductance": 0.22745098039215686,
+    "mincut": 1,
+    "mincut_over_log10n": 0.3884956692397802
   },
   {
     "com_id": "18",
@@ -96,7 +116,9 @@
     "c_boundary": 318,
     "edge_density": 0.008108944599195296,
     "degree_density": 1.4555555555555555,
-    "conductance": 0.232796486090776
+    "conductance": 0.232796486090776,
+    "mincut": 1,
+    "mincut_over_log10n": 0.3911900096721123
   },
   {
     "com_id": "19",
@@ -105,7 +127,9 @@
     "c_boundary": 167,
     "edge_density": 0.011462894105740248,
     "degree_density": 1.7251655629139073,
-    "conductance": 0.1381306865177833
+    "conductance": 0.1381306865177833,
+    "mincut": 1,
+    "mincut_over_log10n": 0.40322467759207314
   },
   {
     "com_id": "2",
@@ -114,7 +138,9 @@
     "c_boundary": 5472,
     "edge_density": 0.0013997304931592414,
     "degree_density": 2.1219914276294096,
-    "conductance": 0.29829917139119055
+    "conductance": 0.29829917139119055,
+    "mincut": 1,
+    "mincut_over_log10n": 0.2872017932187173
   },
   {
     "com_id": "20",
@@ -123,7 +149,9 @@
     "c_boundary": 55,
     "edge_density": 0.01064653503677894,
     "degree_density": 1.5277777777777777,
-    "conductance": 0.058823529411764705
+    "conductance": 0.058823529411764705,
+    "mincut": 1,
+    "mincut_over_log10n": 0.40660447853571624
   },
   {
     "com_id": "21",
@@ -132,7 +160,9 @@
     "c_boundary": 156,
     "edge_density": 0.013544658369676985,
     "degree_density": 1.6050420168067228,
-    "conductance": 0.16956521739130434
+    "conductance": 0.16956521739130434,
+    "mincut": 1,
+    "mincut_over_log10n": 0.42077324575196634
   },
   {
     "com_id": "22",
@@ -141,7 +171,9 @@
     "c_boundary": 125,
     "edge_density": 0.01324236088184586,
     "degree_density": 1.5427350427350428,
-    "conductance": 0.14757969303423848
+    "conductance": 0.14757969303423848,
+    "mincut": 1,
+    "mincut_over_log10n": 0.42208057863209153
   },
   {
     "com_id": "23",
@@ -150,7 +182,9 @@
     "c_boundary": 55,
     "edge_density": 0.016797488226059653,
     "degree_density": 1.6377551020408163,
-    "conductance": 0.07890961262553801
+    "conductance": 0.07890961262553801,
+    "mincut": 1,
+    "mincut_over_log10n": 0.43625143477457795
   },
   {
     "com_id": "24",
@@ -159,7 +193,9 @@
     "c_boundary": 121,
     "edge_density": 0.015425633212721387,
     "degree_density": 1.3651685393258426,
-    "conductance": 0.19934102141680396
+    "conductance": 0.19934102141680396,
+    "mincut": 1,
+    "mincut_over_log10n": 0.44436149650910334
   },
   {
     "com_id": "25",
@@ -168,7 +204,9 @@
     "c_boundary": 190,
     "edge_density": 0.023167592467145372,
     "degree_density": 1.401639344262295,
-    "conductance": 0.35714285714285715
+    "conductance": 0.35714285714285715,
+    "mincut": 1,
+    "mincut_over_log10n": 0.47930370653109755
   },
   {
     "com_id": "26",
@@ -177,7 +215,9 @@
     "c_boundary": 94,
     "edge_density": 0.02461603197980223,
     "degree_density": 1.1938775510204083,
-    "conductance": 0.2865853658536585
+    "conductance": 0.2865853658536585,
+    "mincut": 1,
+    "mincut_over_log10n": 0.5022031461958567
   },
   {
     "com_id": "27",
@@ -186,7 +226,9 @@
     "c_boundary": 40,
     "edge_density": 0.04386317907444668,
     "degree_density": 1.5352112676056338,
-    "conductance": 0.15503875968992248
+    "conductance": 0.15503875968992248,
+    "mincut": 1,
+    "mincut_over_log10n": 0.5401731209973589
   },
   {
     "com_id": "28",
@@ -195,7 +237,9 @@
     "c_boundary": 61,
     "edge_density": 0.04941176470588235,
     "degree_density": 1.2352941176470589,
-    "conductance": 0.32620320855614976
+    "conductance": 0.32620320855614976,
+    "mincut": 1,
+    "mincut_over_log10n": 0.5856274687844196
   },
   {
     "com_id": "29",
@@ -204,7 +248,9 @@
     "c_boundary": 30,
     "edge_density": 0.05263157894736842,
     "degree_density": 1.0,
-    "conductance": 0.2777777777777778
+    "conductance": 0.2777777777777778,
+    "mincut": 1,
+    "mincut_over_log10n": 0.6285099898418801
   },
   {
     "com_id": "3",
@@ -213,7 +259,9 @@
     "c_boundary": 5867,
     "edge_density": 0.0017970481478870486,
     "degree_density": 2.5455187014820044,
-    "conductance": 0.2890859817689086
+    "conductance": 0.2890859817689086,
+    "mincut": 1,
+    "mincut_over_log10n": 0.2896535872530135
   },
   {
     "com_id": "30",
@@ -222,7 +270,9 @@
     "c_boundary": 6,
     "edge_density": 0.25,
     "degree_density": 1.0,
-    "conductance": 0.25
+    "conductance": 0.25,
+    "mincut": 1,
+    "mincut_over_log10n": 1.0479516371446924
   },
   {
     "com_id": "31",
@@ -231,7 +281,9 @@
     "c_boundary": 2,
     "edge_density": 0.3333333333333333,
     "degree_density": 0.8333333333333334,
-    "conductance": 0.16666666666666666
+    "conductance": 0.16666666666666666,
+    "mincut": 1,
+    "mincut_over_log10n": 1.2850972089384687
   },
   {
     "com_id": "32",
@@ -240,7 +292,9 @@
     "c_boundary": 2,
     "edge_density": 0.4,
     "degree_density": 0.8,
-    "conductance": 0.2
+    "conductance": 0.2,
+    "mincut": 1,
+    "mincut_over_log10n": 1.430676558073393
   },
   {
     "com_id": "33",
@@ -249,7 +303,9 @@
     "c_boundary": 1,
     "edge_density": 0.4,
     "degree_density": 0.8,
-    "conductance": 0.1111111111111111
+    "conductance": 0.1111111111111111,
+    "mincut": 1,
+    "mincut_over_log10n": 1.430676558073393
   },
   {
     "com_id": "34",
@@ -258,7 +314,9 @@
     "c_boundary": 6,
     "edge_density": 0.4,
     "degree_density": 0.8,
-    "conductance": 0.42857142857142855
+    "conductance": 0.42857142857142855,
+    "mincut": 1,
+    "mincut_over_log10n": 1.430676558073393
   },
   {
     "com_id": "35",
@@ -267,7 +325,9 @@
     "c_boundary": 6,
     "edge_density": 0.4,
     "degree_density": 0.8,
-    "conductance": 0.42857142857142855
+    "conductance": 0.42857142857142855,
+    "mincut": 1,
+    "mincut_over_log10n": 1.430676558073393
   },
   {
     "com_id": "36",
@@ -276,7 +336,9 @@
     "c_boundary": 4,
     "edge_density": 0.5,
     "degree_density": 0.75,
-    "conductance": 0.4
+    "conductance": 0.4,
+    "mincut": 1,
+    "mincut_over_log10n": 1.660964047443681
   },
   {
     "com_id": "37",
@@ -285,7 +347,9 @@
     "c_boundary": 1,
     "edge_density": 0.5,
     "degree_density": 0.75,
-    "conductance": 0.14285714285714285
+    "conductance": 0.14285714285714285,
+    "mincut": 1,
+    "mincut_over_log10n": 1.660964047443681
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   {
     "com_id": "38",
@@ -294,7 +358,9 @@
     "c_boundary": 3,
     "edge_density": 0.5,
     "degree_density": 0.75,
-    "conductance": 0.3333333333333333
+    "conductance": 0.3333333333333333,
+    "mincut": 1,
+    "mincut_over_log10n": 1.660964047443681
   },
   {
     "com_id": "39",
@@ -303,7 +369,9 @@
     "c_boundary": 5,
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     "degree_density": 0.75,
-    "conductance": 0.45454545454545453
+    "conductance": 0.45454545454545453,
+    "mincut": 1,
+    "mincut_over_log10n": 1.660964047443681
   },
   {
     "com_id": "4",
@@ -312,7 +380,9 @@
     "c_boundary": 3414,
     "edge_density": 0.0014043493863960003,
     "degree_density": 1.3432601880877744,
-    "conductance": 0.39901823281907434
+    "conductance": 0.39901823281907434,
+    "mincut": 1,
+    "mincut_over_log10n": 0.30469765165881185
   },
   {
     "com_id": "40",
@@ -321,7 +391,9 @@
     "c_boundary": 3,
     "edge_density": 0.5,
     "degree_density": 0.75,
-    "conductance": 0.3333333333333333
+    "conductance": 0.3333333333333333,
+    "mincut": 1,
+    "mincut_over_log10n": 1.660964047443681
   },
   {
     "com_id": "41",
@@ -330,7 +402,9 @@
     "c_boundary": 3,
     "edge_density": 0.5,
     "degree_density": 0.75,
-    "conductance": 0.3333333333333333
+    "conductance": 0.3333333333333333,
+    "mincut": 1,
+    "mincut_over_log10n": 1.660964047443681
   },
   {
     "com_id": "42",
@@ -339,7 +413,9 @@
     "c_boundary": 2,
     "edge_density": 1.0,
     "degree_density": 1.0,
-    "conductance": 0.25
+    "conductance": 0.25,
+    "mincut": 2,
+    "mincut_over_log10n": 4.19180654857877
   },
   {
     "com_id": "43",
@@ -348,7 +424,9 @@
     "c_boundary": 1,
     "edge_density": 0.6666666666666666,
     "degree_density": 0.6666666666666666,
-    "conductance": 0.2
+    "conductance": 0.2,
+    "mincut": 1,
+    "mincut_over_log10n": 2.095903274289385
   },
   {
     "com_id": "44",
@@ -357,7 +435,9 @@
     "c_boundary": 1,
     "edge_density": 0.6666666666666666,
     "degree_density": 0.6666666666666666,
-    "conductance": 0.2
+    "conductance": 0.2,
+    "mincut": 1,
+    "mincut_over_log10n": 2.095903274289385
   },
   {
     "com_id": "45",
@@ -366,7 +446,9 @@
     "c_boundary": 2,
     "edge_density": 0.6666666666666666,
     "degree_density": 0.6666666666666666,
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+    "conductance": 0.3333333333333333,
+    "mincut": 1,
+    "mincut_over_log10n": 2.095903274289385
   },
   {
     "com_id": "46",
@@ -375,7 +457,9 @@
     "c_boundary": 1,
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+    "conductance": 0.2,
+    "mincut": 1,
+    "mincut_over_log10n": 2.095903274289385
   },
   {
     "com_id": "47",
@@ -384,7 +468,9 @@
     "c_boundary": 2,
     "edge_density": 0.6666666666666666,
     "degree_density": 0.6666666666666666,
-    "conductance": 0.3333333333333333
+    "conductance": 0.3333333333333333,
+    "mincut": 1,
+    "mincut_over_log10n": 2.095903274289385
   },
   {
     "com_id": "48",
@@ -393,7 +479,9 @@
     "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": "49",
@@ -402,7 +490,9 @@
     "c_boundary": 3,
     "edge_density": 1.0,
     "degree_density": 1.0,
-    "conductance": 0.3333333333333333
+    "conductance": 0.3333333333333333,
+    "mincut": 2,
+    "mincut_over_log10n": 4.19180654857877
   },
   {
     "com_id": "5",
@@ -411,7 +501,9 @@
     "c_boundary": 2273,
     "edge_density": 0.0020410753063095435,
     "degree_density": 1.8737071311921611,
-    "conductance": 0.24822540133231408
+    "conductance": 0.24822540133231408,
+    "mincut": 1,
+    "mincut_over_log10n": 0.30636230349960514
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   {
     "com_id": "6",
@@ -420,7 +512,9 @@
     "c_boundary": 815,
     "edge_density": 0.0022016806546568007,
     "degree_density": 1.520260492040521,
-    "conductance": 0.16244767789515646
+    "conductance": 0.16244767789515646,
+    "mincut": 1,
+    "mincut_over_log10n": 0.3184198181618358
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   {
     "com_id": "7",
@@ -429,7 +523,9 @@
     "c_boundary": 532,
     "edge_density": 0.0024604868857552344,
     "degree_density": 1.5537974683544304,
-    "conductance": 0.11928251121076233
+    "conductance": 0.11928251121076233,
+    "mincut": 1,
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   {
     "com_id": "8",
@@ -438,7 +534,9 @@
     "c_boundary": 2113,
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     "degree_density": 1.7374517374517375,
-    "conductance": 0.36985821809907227
+    "conductance": 0.36985821809907227,
+    "mincut": 1,
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   },
   {
     "com_id": "9",
@@ -447,6 +545,8 @@
     "c_boundary": 868,
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+    "conductance": 0.18869565217391304,
+    "mincut": 1,
+    "mincut_over_log10n": 0.3350109423454273
   }
 ]
\ No newline at end of file