Table 5 Network analysis of learned influence networks for different spheres of legislation. Various centrality measures and network-level properties are shown

Number of edges

1191

1071

1280

1076

Network diameter

5

5

4

5

Avg. (shortest) path length

2.2295

2.5132

2.1506

2.5476

Avg. clustering coefficient

0.1867

0.2057

0.174

0.2176

Modularity

0.7861

0.8904

0.8724

0.8857

Degree centrality

 Degree (1)

0.5784: LEE R-UT

0.3529: TOOMEY R-PA

0.3725: LANKFORD R-OK

0.3725: COTTON R-AR

 Degree (2)

0.4216: PAUL R-KY

0.3333: PERDUE R-GA

0.3627: SASSE R-NE

0.2941: LEAHY D-VT

 Degree (3)

0.4118: SANDERS I-VT

0.3235: ENZI R-WY

0.3529: WARNER D-VA

0.2843: CAPITO R-WV

 Degree (4)

0.3824: MORAN R-KS

0.3137: LANKFORD R-OK

0.3333: CAPITO R-WV

0.2843: MURKOWSKI R-AK

 Degree (5)

0.3725: MANCHIN D-WV

0.3137: YOUNG R-IN

0.3235: TOOMEY R-PA

0.2745: AYOTTE R-NH

 Degree (6)

0.3627: RUBIO R-FL

0.3039: COTTON R-AR

0.3235: MURKOWSKI R-AK

0.2745: SHELBY R-AL

 Degree (7)

0.3529: CRUZ R-TX

0.2941: CASEY D-PA

0.3235: COTTON R-AR

0.2647: PERDUE R-GA

 Degree (8)

0.3333: ALEXANDER R-TN

0.2843: CASSIDY R-LA

0.3137: BROWN D-OH

0.2549: ALEXANDER R-TN

 Degree (9)

0.3333: ENZI R-WY

0.2843: WICKER R-MS

0.3137: FEINSTEIN D-CA

0.2549: PETERS D-MI

 Degree (10)

0.3235: LEAHY D-VT

0.2745: CORKER R-TN

0.3137: PAUL R-KY

0.2549: PAUL R-KY

Closeness centrality

 Closeness (1)

0.5862: LEE R-UT

0.5126: PERDUE R-GA

0.5514: WARNER D-VA

0.5204: COTTON R-AR

 Closeness (2)

0.5635: RUBIO R-FL

0.4951: COTTON R-AR

0.5426: LANKFORD R-OK

0.5178: KIRK R-IL

 Closeness (3)

0.5574: PAUL R-KY

0.4766: COLLINS R-ME

0.5368: SASSE R-NE

0.4951: MURKOWSKI R-AK

 Closeness (4)

0.5455: SANDERS I-VT

0.47: ENZI R-WY

0.5368: BENNET D-CO

0.4928: AYOTTE R-NH

 Closeness (5)

0.5455: BALDWIN D-WI

0.4636: SASSE R-NE

0.534: KING I-ME

0.4766: SULLIVAN R-AK

 Closeness (6)

0.5397: ENZI R-WY

0.4636: MANCHIN D-WV

0.5231: MURKOWSKI R-AK

0.4744: MCCONNELL R-KY

 Closeness (7)

0.5368: MORAN R-KS

0.4615: FLAKE R-AZ

0.5178: COTTON R-AR

0.4722: PAUL R-KY

 Closeness (8)

0.5285: CORKER R-TN

0.4595: SHELBY R-AL

0.5152: BROWN D-OH

0.4636: COLLINS R-ME

 Closeness (9)

0.5258: CASEY D-PA

0.4595: YOUNG R-IN

0.5126: CASEY D-PA

0.4554: CAPITO R-WV

 Closeness (10)

0.5231: DURBIN D-IL

0.4595: HEITKAMP D-ND

0.51: CARPER D-DE

0.4554: SANDERS I-VT

Betweenness centrality

 Betweenness (1)

0.0696: LEE R-UT

0.0538: PERDUE R-GA

0.0278: LANKFORD R-OK

0.0685: SANDERS I-VT

 Betweenness (2)

0.0362: PERDUE R-GA

0.0468: HEITKAMP D-ND

0.0272: SASSE R-NE

0.0641: WYDEN D-OR

 Betweenness (3)

0.033: MORAN R-KS

0.0452: GILLIBRAND D-NY

0.0265: WARNER D-VA

0.0559: COTTON R-AR

 Betweenness (4)

0.0314: KING I-ME

0.045: ENZI R-WY

0.0226: BENNET D-CO

0.0533: MARKEY D-MA

 Betweenness (5)

0.0301: MANCHIN D-WV

0.0434: COLLINS R-ME

0.0206: MURKOWSKI R-AK

0.0532: ALEXANDER R-TN

 Betweenness (6)

0.0288: DURBIN D-IL

0.0383: MERKLEY D-OR

0.0196: BROWN D-OH

0.0421: MURKOWSKI R-AK

 Betweenness (7)

0.0283: RUBIO R-FL

0.0382: COTTON R-AR

0.0194: CORNYN R-TX

0.0381: PAUL R-KY

 Betweenness (8)

0.0283: PAUL R-KY

0.0381: SANDERS I-VT

0.0193: SCHATZ D-HI

0.0376: SASSE R-NE

 Betweenness (9)

0.0253: SANDERS I-VT

0.0344: LEE R-UT

0.0187: SANDERS I-VT

0.0347: HARRIS D-CA

 Betweenness (10)

0.0249: CRUZ R-TX

0.034: TESTER D-MT

0.0185: WICKER R-MS

0.032: AYOTTE R-NH

Eigenvector centrality

 Eigenvector (1)

0.271: LEE R-UT

0.2114: COTTON R-AR

0.181: WARNER D-VA

0.2029: KIRK R-IL

 Eigenvector (2)

0.2291: SANDERS I-VT

0.2061: PERDUE R-GA

0.1703: CORNYN R-TX

0.2017: HOEVEN R-ND

 Eigenvector (3)

0.228: PAUL R-KY

0.1866: SULLIVAN R-AK

0.1675: LANKFORD R-OK

0.1727: GARDNER R-CO

 Eigenvector (4)

0.1894: BALDWIN D-WI

0.1865: ENZI R-WY

0.1567: BENNET D-CO

0.1724: PORTMAN R-OH

 Eigenvector (5)

0.1892: RUBIO R-FL

0.183: YOUNG R-IN

0.1551: JOHNSON R-WI

0.1715: CAPITO R-WV

 Eigenvector (6)

0.1696: ENZI R-WY

0.1758: THUNE R-SD

0.1541: SASSE R-NE

0.1706: COTTON R-AR

 Eigenvector (7)

0.1681: BARRASSO R-WY

0.1734: WICKER R-MS

0.1525: MURKOWSKI R-AK

0.1706: ROBERTS R-KS

 Eigenvector (8)

0.161: CASEY D-PA

0.1674: MORAN R-KS

0.1454: KING I-ME

0.1683: FISCHER R-NE

 Eigenvector (9)

0.1607: MORAN R-KS

0.1653: JOHNSON R-WI

0.1426: COTTON R-AR

0.1682: MURKOWSKI R-AK

 Eigenvector (10)

0.1602: MANCHIN D-WV

0.163: GARDNER R-CO

0.1379: BOOZMAN R-AR

0.1646: ISAKSON R-GA