In [1]:
import sys

sys.path.append('../../code/')
import os
import json
from datetime import datetime
import time
from math import *

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import scipy.stats as stats
import igraph as ig

from load_data import load_citation_network_igraph, case_info
from helper_functions import rankdata_reverse

%load_ext autoreload
%autoreload 2
%matplotlib inline

data_dir = '../../data/'
court_name = 'scotus'

load into igraph


In [2]:
g_d = load_citation_network_igraph(data_dir, 'scotus', directed=True)
g_u = load_citation_network_igraph(data_dir, 'scotus', directed=False)


0 seconds for 250465 edges
0 seconds for 250465 edges

In [3]:
case_metrics = pd.DataFrame(index=range(len(g_d.vs)))
case_metrics['id'] = g_d.vs['name']
case_metrics['year'] = g_d.vs['year']


# run on directed graph
case_metrics['authority_d'] = g_d.authority_score()
case_metrics['indegree_d'] = g_d.indegree()
case_metrics['outdegree_d'] = g_d.outdegree()
case_metrics['hubs_d'] = g_d.hub_score()
case_metrics['betweenness_d'] = g_d.betweenness()
case_metrics['eigen_d'] = g_d.eigenvector_centrality()
case_metrics['closeness_d'] = g_d.closeness()
case_metrics['pagerank_d'] = g_d.pagerank()

# run on undirected graph
case_metrics['authority_u'] = g_u.authority_score()
case_metrics['indegree_u'] = g_u.indegree()
case_metrics['outdegree_u'] = g_u.outdegree()
case_metrics['hubs_u'] = g_u.hub_score()
case_metrics['betweenness_u'] = g_u.betweenness()
case_metrics['eigen_u'] = g_u.eigenvector_centrality()
case_metrics['closeness_u'] = g_u.closeness()
case_metrics['pagerank_u'] = g_u.pagerank()

In [ ]:
case_metrics[case_metrics]

In [7]:
# case_metrics.to_csv(data_dir + 'analysis/case_metrics.csv', index=False)
# pd.read_csv(data_dir + 'analysis/case_metrics.csv')

In [26]:
case_ranks = pd.DataFrame(index=case_metrics.index,
                         columns=case_metrics.columns)
case_ranks['id'] = case_metrics['id']
case_ranks['year'] = case_metrics['year']


for col in case_metrics.columns[2:]:
    case_ranks[col] = rankdata_reverse(case_metrics[col].tolist())

In [33]:
case_metrics.sort_values('pagerank_d', ascending=False)


Out[33]:
id year authority_d indegree_d outdegree_d hubs_d betweenness_d eigen_d closeness_d pagerank_d authority_u indegree_u outdegree_u hubs_u betweenness_u eigen_u closeness_u pagerank_u
18886 85131 1816 1.157353e-01 181 0 2.034008e-14 0.000000e+00 1.000000e+00 0.000176 0.001634 1.610516e-01 181 181 1.610516e-01 1.239950e+06 1.610516e-01 0.000176 0.000237
24956 91573 1886 5.042884e-01 234 0 2.637747e-14 0.000000e+00 1.070919e-02 0.000176 0.001280 4.603153e-01 234 234 4.603153e-01 1.817754e+06 4.603153e-01 0.000176 0.000279
19247 85534 1827 6.768311e-02 124 0 1.398579e-14 0.000000e+00 9.276676e-01 0.000176 0.001265 8.835111e-02 124 124 8.835111e-02 4.601963e+05 8.835111e-02 0.000176 0.000162
18914 85160 1816 1.025219e-01 94 0 1.061630e-14 0.000000e+00 4.708626e-01 0.000176 0.001016 9.440510e-02 94 94 9.440510e-02 1.163621e+06 9.440510e-02 0.000176 0.000161
22148 88661 1873 2.433521e-01 124 0 1.398579e-14 0.000000e+00 1.402792e-01 0.000176 0.000984 2.555743e-01 124 124 2.555743e-01 6.557200e+05 2.555743e-01 0.000176 0.000153
23084 89675 1878 1.169660e-01 107 3 1.264144e-02 1.678772e+04 9.907676e-02 0.000176 0.000890 1.410844e-01 110 110 1.410844e-01 6.610216e+05 1.410844e-01 0.000176 0.000156
22280 88804 1874 7.094948e-02 93 0 1.049883e-14 0.000000e+00 1.599104e-01 0.000176 0.000866 7.668985e-02 93 93 7.668985e-02 4.228084e+05 7.668985e-02 0.000176 0.000138
19060 85330 1821 1.668248e-01 157 0 1.769310e-14 0.000000e+00 2.965331e-01 0.000176 0.000860 1.592372e-01 157 157 1.592372e-01 2.573332e+06 1.592372e-01 0.000176 0.000225
31365 98094 1914 2.838527e-01 138 11 4.539784e-02 2.698975e+05 0.000000e+00 0.000176 0.000785 3.104819e-01 149 149 3.104819e-01 2.504442e+05 3.104819e-01 0.000176 0.000170
16953 1528394 1867 6.914532e-02 55 1 1.495658e-06 1.531319e+04 3.937228e-02 0.000176 0.000782 7.742759e-02 56 56 7.742759e-02 2.696736e+05 7.742759e-02 0.000176 0.000084
20646 87010 1856 1.078678e-01 91 7 5.346751e-03 8.693994e+04 9.354083e-02 0.000176 0.000762 1.235994e-01 98 98 1.235994e-01 7.243641e+05 1.235994e-01 0.000176 0.000145
20340 86696 1852 9.517271e-02 133 3 1.007799e-02 8.096910e+03 8.142094e-01 0.000176 0.000761 1.069178e-01 136 136 1.069178e-01 5.620106e+05 1.069178e-01 0.000176 0.000171
22097 88605 1873 3.028301e-02 60 0 6.755827e-15 0.000000e+00 5.557133e-01 0.000176 0.000755 4.002398e-02 60 60 4.002398e-02 6.910560e+04 4.002398e-02 0.000176 0.000075
6248 106545 1963 4.252189e-01 229 50 4.136222e-01 2.394818e+06 0.000000e+00 0.000176 0.000706 5.394175e-01 279 279 5.394175e-01 3.013197e+06 5.394175e-01 0.000176 0.000464
9366 109532 1976 2.349215e-01 294 22 9.252564e-02 1.412721e+06 4.711740e-15 0.000176 0.000705 2.253614e-01 316 316 2.253614e-01 2.300226e+06 2.253614e-01 0.000176 0.000586
12572 112790 1992 8.146171e-04 85 5 3.811237e-05 1.437630e+06 4.079599e-17 0.000176 0.000690 8.584490e-04 90 90 8.584490e-04 2.150066e+06 8.584490e-04 0.000176 0.001050
25087 91704 1886 4.235948e-01 169 6 1.396799e-02 2.509755e+04 5.332230e-02 0.000176 0.000690 3.971038e-01 175 175 3.971038e-01 8.016265e+05 3.971038e-01 0.000176 0.000208
21311 87754 1867 4.279166e-05 3 1 2.416773e-03 3.017243e+02 1.236524e-02 0.000176 0.000684 2.361520e-03 4 4 2.361520e-03 5.782432e+03 2.361520e-03 0.000176 0.000013
19169 85451 1824 8.988614e-02 169 0 1.906472e-14 0.000000e+00 3.165638e-01 0.000176 0.000673 9.165637e-02 169 169 9.165637e-02 1.976900e+06 9.165637e-02 0.000176 0.000257
22595 89173 1876 4.825390e-02 78 2 1.959177e-03 2.412660e+03 7.280131e-01 0.000176 0.000663 6.065155e-02 80 80 6.065155e-02 9.136585e+04 6.065155e-02 0.000176 0.000098
24456 91054 1884 2.292375e-01 108 4 1.105956e-02 1.312497e+04 4.038331e-02 0.000176 0.000651 2.449008e-01 112 112 2.449008e-01 4.124137e+05 2.449008e-01 0.000176 0.000142
21305 87748 1866 2.671919e-02 65 1 4.045191e-03 5.497231e+02 6.781484e-01 0.000176 0.000647 4.454266e-02 66 66 4.454266e-02 1.420346e+05 4.454266e-02 0.000176 0.000092
23749 90336 1881 1.083564e-01 78 3 1.735803e-02 1.311361e+04 4.498431e-02 0.000176 0.000645 1.233711e-01 81 81 1.233711e-01 2.158014e+05 1.233711e-01 0.000176 0.000107
24646 91255 1884 2.164625e-02 38 0 4.279645e-15 0.000000e+00 1.390358e-01 0.000176 0.000620 4.151299e-02 38 38 4.151299e-02 3.972514e+04 4.151299e-02 0.000176 0.000054
23449 90041 1880 2.046451e-01 109 6 1.589505e-02 4.081001e+04 6.099231e-02 0.000176 0.000611 2.284839e-01 115 115 2.284839e-01 3.612735e+05 2.284839e-01 0.000176 0.000141
29887 96594 1907 2.141466e-02 94 7 5.585695e-04 1.328126e+05 7.693762e-04 0.000176 0.000600 2.428465e-02 101 101 2.428465e-02 5.835138e+05 2.428465e-02 0.000176 0.000158
21607 88075 1869 2.577020e-02 49 0 5.513712e-15 0.000000e+00 4.163202e-01 0.000176 0.000593 3.191535e-02 49 49 3.191535e-02 6.304147e+04 3.191535e-02 0.000176 0.000064
23065 89656 1878 5.850716e-02 125 11 1.671354e-03 8.305933e+04 2.381896e-02 0.000176 0.000591 6.211743e-02 136 136 6.211743e-02 1.522584e+06 6.211743e-02 0.000176 0.000239
23702 90287 1881 3.564786e-02 78 4 7.177416e-03 5.304813e+03 3.849092e-01 0.000176 0.000584 5.532546e-02 82 82 5.532546e-02 2.417049e+05 5.532546e-02 0.000176 0.000111
22611 89190 1876 1.196303e-02 46 0 5.187514e-15 0.000000e+00 4.415659e-02 0.000176 0.000571 1.435860e-02 46 46 1.435860e-02 2.375722e+05 1.435860e-02 0.000176 0.000078
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
15576 141682 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15575 141681 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15574 141680 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15573 141679 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15572 141678 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15571 141677 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
25355 91982 1887 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15570 141676 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15583 141689 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15584 141690 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15585 141691 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15586 141692 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15601 141707 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15600 141706 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15599 141705 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15598 141704 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15597 141703 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15596 141702 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15595 141701 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
25324 91951 1887 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15594 141700 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15593 141699 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
25327 91954 1887 5.469286e-17 0 1 1.465486e-06 0.000000e+00 2.926498e-19 0.000176 0.000010 1.018018e-06 1 1 1.018018e-06 0.000000e+00 1.018018e-06 0.000176 0.000009
15592 141698 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15591 141697 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15590 141696 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15589 141695 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15588 141694 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
15587 141693 2005 5.469286e-17 0 0 1.126011e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145651e-16 0 0 1.145651e-16 0.000000e+00 3.592139e-17 0.000030 0.000005
14093 122113 2002 5.469286e-17 0 1 1.124661e-16 0.000000e+00 2.926498e-19 0.000030 0.000010 1.145666e-16 1 1 1.145666e-16 0.000000e+00 3.796395e-17 0.000030 0.000034

33248 rows × 18 columns


In [39]:
case_info(88661)


Slaughter-House Cases
1873-04-14

https://www.courtlistener.com/opinion/88661/slaughter-house-cases/


In [27]:
erie = case_metrics[case_metrics.id == 103012]
case_ranks[case_ranks.id == 103012]


Out[27]:
id year authority_d indegree_d outdegree_d hubs_d betweenness_d eigen_d closeness_d pagerank_d authority_u indegree_u outdegree_u hubs_u betweenness_u eigen_u closeness_u pagerank_u
2891 103012 1938 197 8 487 4387 4 23887 2 94 561 12 12 561 2 561 2 9

In [28]:
detroit = case_metrics[case_metrics.id == 96405]
case_ranks[case_ranks.id == 96405]


Out[28]:
id year authority_d indegree_d outdegree_d hubs_d betweenness_d eigen_d closeness_d pagerank_d authority_u indegree_u outdegree_u hubs_u betweenness_u eigen_u closeness_u pagerank_u
29701 96405 1906 18 1 1542 13214 489 6669 5 65 211 1 1 211 1 211 5 2

In [40]:
slaughter = case_metrics[case_metrics.id == 88661]
case_ranks[case_ranks.id == 88661]


Out[40]:
id year authority_d indegree_d outdegree_d hubs_d betweenness_d eigen_d closeness_d pagerank_d authority_u indegree_u outdegree_u hubs_u betweenness_u eigen_u closeness_u pagerank_u
22148 88661 1873 117 51 24208 23174 18951 45 53 5 277 186 186 277 173 277 53 253

closeness


In [5]:
plt.scatter(case_metrics['year'], case_metrics['closeness_d'])
plt.xlim([1750, 2016])
plt.ylim([0, .0003])


Out[5]:
(0, 0.0003)

Authority


In [22]:
plt.figure(figsize=[10, 10])
plt.scatter(case_metrics['year'],
            case_metrics['authority_d'],
            marker='.',
            color='black')

# plt.scatter(detroit['year'],
#             detroit['authority_d'],
#             marker='.',
#             color='red',
#             s=1000)


plt.xlim([1750, 2016])
plt.ylim([0, 1])

plt.xlabel('year')
plt.ylabel('authority score ')


Out[22]:
<matplotlib.text.Text at 0x111cbcfd0>

Page rank


In [18]:
plt.figure(figsize=[10, 10])
plt.scatter(case_metrics['year'],
            case_metrics['pagerank_d'],
            marker='.',
            color='black')
plt.xlim([1750, 2016])
plt.ylim([0, .002])

plt.xlabel('year')
plt.ylabel('pagerank ')


Out[18]:
<matplotlib.text.Text at 0x11183b390>

In [41]:
plt.figure(figsize=[10, 10])
plt.scatter(case_metrics['year'],
            case_metrics['pagerank_d'],
            marker='.',
            color='black')

plt.scatter(slaughter['year'],
            slaughter['pagerank_d'],
            marker='.',
            color='red',
            s=1000)

plt.xlim([1750, 2016])
plt.ylim([0, .002])

plt.xlabel('year')
plt.ylabel('pagerank ')


Out[41]:
<matplotlib.text.Text at 0x118738190>

rank correlations


In [50]:
kendall_tau = pd.DataFrame(index=case_ranks.columns[1:], columns=case_ranks.columns[1:])
for ra in case_ranks.columns[1:]:
    for rb in case_ranks.columns[1:]:
        kendall_tau.loc[ra, rb] = stats.kendalltau(case_ranks[ra], case_ranks[rb]).correlation

kendall_tau


Out[50]:
authority_d indegree_d outdegree_d hubs_d betweenness_d eigen_d closeness_d pagerank_d authority_u indegree_u outdegree_u hubs_u betweenness_u eigen_u closeness_u pagerank_u
authority_d 1 0.741248 0.495374 0.556081 0.573691 0.383767 0.732838 0.513871 0.75579 0.699461 0.699461 0.75579 0.554221 0.749174 0.732838 0.542936
indegree_d 0.741248 1 0.431341 0.443222 0.640582 0.538265 0.638519 0.7367 0.573564 0.73274 0.73274 0.573564 0.630091 0.566826 0.638519 0.657485
outdegree_d 0.495374 0.431341 1 0.73232 0.657041 0.114876 0.661082 0.246336 0.621001 0.740664 0.740664 0.621001 0.597519 0.614242 0.661082 0.633759
hubs_d 0.556081 0.443222 0.73232 1 0.523644 0.1008 0.704172 0.242103 0.770513 0.663756 0.663756 0.770513 0.499844 0.776026 0.704172 0.489353
betweenness_d 0.573691 0.640582 0.657041 0.523644 1 0.357284 0.587297 0.498246 0.509853 0.67153 0.67153 0.509853 0.687608 0.509676 0.587297 0.630068
eigen_d 0.383767 0.538265 0.114876 0.1008 0.357284 1 0.29683 0.610198 0.227622 0.342654 0.342654 0.227622 0.378185 0.222044 0.29683 0.319571
closeness_d 0.732838 0.638519 0.661082 0.704172 0.587297 0.29683 1 0.423819 0.84909 0.796893 0.796893 0.84909 0.642861 0.836481 1 0.611534
pagerank_d 0.513871 0.7367 0.246336 0.242103 0.498246 0.610198 0.423819 1 0.363299 0.507507 0.507507 0.363299 0.506861 0.35677 0.423819 0.539262
authority_u 0.75579 0.573564 0.621001 0.770513 0.509853 0.227622 0.84909 0.363299 1 0.719045 0.719045 1 0.535905 0.987339 0.84909 0.521697
indegree_u 0.699461 0.73274 0.740664 0.663756 0.67153 0.342654 0.796893 0.507507 0.719045 1 1 0.719045 0.736327 0.706333 0.796893 0.804298
outdegree_u 0.699461 0.73274 0.740664 0.663756 0.67153 0.342654 0.796893 0.507507 0.719045 1 1 0.719045 0.736327 0.706333 0.796893 0.804298
hubs_u 0.75579 0.573564 0.621001 0.770513 0.509853 0.227622 0.84909 0.363299 1 0.719045 0.719045 1 0.535905 0.987339 0.84909 0.521697
betweenness_u 0.554221 0.630091 0.597519 0.499844 0.687608 0.378185 0.642861 0.506861 0.535905 0.736327 0.736327 0.535905 1 0.535722 0.642861 0.730037
eigen_u 0.749174 0.566826 0.614242 0.776026 0.509676 0.222044 0.836481 0.35677 0.987339 0.706333 0.706333 0.987339 0.535722 1 0.836481 0.509353
closeness_u 0.732838 0.638519 0.661082 0.704172 0.587297 0.29683 1 0.423819 0.84909 0.796893 0.796893 0.84909 0.642861 0.836481 1 0.611534
pagerank_u 0.542936 0.657485 0.633759 0.489353 0.630068 0.319571 0.611534 0.539262 0.521697 0.804298 0.804298 0.521697 0.730037 0.509353 0.611534 1

In [53]:
spearman = pd.DataFrame(index=case_ranks.columns[1:], columns=case_ranks.columns[1:])
for ra in case_ranks.columns[1:]:
    for rb in case_ranks.columns[1:]:
        spearman.loc[ra, rb] = stats.spearmanr(case_ranks[ra], case_ranks[rb]).correlation

spearman


Out[53]:
authority_d indegree_d outdegree_d hubs_d betweenness_d eigen_d closeness_d pagerank_d authority_u indegree_u outdegree_u hubs_u betweenness_u eigen_u closeness_u pagerank_u
authority_d 1 0.893353 0.646366 0.716477 0.742643 0.564037 0.884967 0.693259 0.880444 0.85769 0.85769 0.880444 0.731801 0.878601 0.884967 0.718019
indegree_d 0.893353 1 0.558302 0.571893 0.778166 0.706149 0.787145 0.878629 0.720841 0.860148 0.860148 0.720841 0.786256 0.717157 0.787145 0.806103
outdegree_d 0.646366 0.558302 1 0.89046 0.798001 0.174348 0.812595 0.33942 0.782417 0.865879 0.865879 0.782417 0.748821 0.778694 0.812595 0.784742
hubs_d 0.716477 0.571893 0.89046 1 0.683605 0.179545 0.874319 0.347262 0.910197 0.830649 0.830649 0.910197 0.673214 0.911839 0.874319 0.655799
betweenness_d 0.742643 0.778166 0.798001 0.683605 1 0.473843 0.745606 0.622252 0.670624 0.821248 0.821248 0.670624 0.811024 0.670608 0.745606 0.775394
eigen_d 0.564037 0.706149 0.174348 0.179545 0.473843 1 0.437299 0.783816 0.346917 0.492559 0.492559 0.346917 0.529987 0.344504 0.437299 0.460419
closeness_d 0.884967 0.787145 0.812595 0.874319 0.745606 0.437299 1 0.578111 0.962619 0.933548 0.933548 0.962619 0.821428 0.95954 1 0.786598
pagerank_d 0.693259 0.878629 0.33942 0.347262 0.622252 0.783816 0.578111 1 0.504383 0.672768 0.672768 0.504383 0.663321 0.496112 0.578111 0.713711
authority_u 0.880444 0.720841 0.782417 0.910197 0.670624 0.346917 0.962619 0.504383 1 0.877085 0.877085 1 0.718204 0.997146 0.962619 0.699756
indegree_u 0.85769 0.860148 0.865879 0.830649 0.821248 0.492559 0.933548 0.672768 0.877085 1 1 0.877085 0.893662 0.872819 0.933548 0.916759
outdegree_u 0.85769 0.860148 0.865879 0.830649 0.821248 0.492559 0.933548 0.672768 0.877085 1 1 0.877085 0.893662 0.872819 0.933548 0.916759
hubs_u 0.880444 0.720841 0.782417 0.910197 0.670624 0.346917 0.962619 0.504383 1 0.877085 0.877085 1 0.718204 0.997146 0.962619 0.699756
betweenness_u 0.731801 0.786256 0.748821 0.673214 0.811024 0.529987 0.821428 0.663321 0.718204 0.893662 0.893662 0.718204 1 0.718194 0.821428 0.86936
eigen_u 0.878601 0.717157 0.778694 0.911839 0.670608 0.344504 0.95954 0.496112 0.997146 0.872819 0.872819 0.997146 0.718194 1 0.95954 0.677476
closeness_u 0.884967 0.787145 0.812595 0.874319 0.745606 0.437299 1 0.578111 0.962619 0.933548 0.933548 0.962619 0.821428 0.95954 1 0.786598
pagerank_u 0.718019 0.806103 0.784742 0.655799 0.775394 0.460419 0.786598 0.713711 0.699756 0.916759 0.916759 0.699756 0.86936 0.677476 0.786598 1

In [ ]: