Table 7 Network analysis of influence networks for different spheres of legislation learned using Irfan and Gordon [28]’s model of ideal points with social interactions. Various centrality measures and network-level properties are shown

Number of edges

1102

1027

1106

1234

Avg. (shortest) path length

2.1641

2.3898

2.2948

2.1806

Avg. clustering coefficient

0.165

0.1747

0.1754

0.1812

Modularity

0.5392

0.6801

0.6887

0.6229

Degree centrality

 Degree (1)

0.451: MANCHIN D-WV

0.4118: MANCHIN D-WV

0.4902: TESTER D-MT

0.5392: CARPER D-DE

 Degree (2)

0.4314: CRUZ R-TX

0.3922: KING I-ME

0.451: DONNELLY D-IN

0.4706: TESTER D-MT

 Degree (3)

0.4118: CORKER R-TN

0.3824: HEITKAMP D-ND

0.3627: KING I-ME

0.451: MANCHIN D-WV

 Degree (4)

0.402: LEE R-UT

0.3627: MENENDEZ D-NJ

0.3627: KLOBUCHAR D-MN

0.451: DURBIN D-IL

 Degree (5)

0.3922: PAUL R-KY

0.3529: HELLER R-NV

0.3627: HEITKAMP D-ND

0.451: PAUL R-KY

 Degree (6)

0.3922: ENZI R-WY

0.3431: FLAKE R-AZ

0.3627: LEE R-UT

0.4314: MCCASKILL D-MO

 Degree (7)

0.3627: SCHATZ D-HI

0.3431: TESTER D-MT

0.3529: COLLINS R-ME

0.4118: HARRIS D-CA

 Degree (8)

0.3529: HELLER R-NV

0.3333: DONNELLY D-IN

0.3529: MCCASKILL D-MO

0.3922: STABENOW D-MI

 Degree (9)

0.3431: BALDWIN D-WI

0.3333: WYDEN D-OR

0.3529: WARNER D-VA

0.3725: HEITKAMP D-ND

 Degree (10)

0.3431: TESTER D-MT

0.3333: FEINSTEIN D-CA

0.3529: CARPER D-DE

0.3627: LEE R-UT

Closeness Centrality

 Closeness (1)

0.5426: MANCHIN D-WV

0.516: MANCHIN D-WV

0.5543: DONNELLY D-IN

0.573: MCCASKILL D-MO

 Closeness (2)

0.5231: HELLER R-NV

0.5133: HEITKAMP D-ND

0.5484: TESTER D-MT

0.5635: CARPER D-DE

 Closeness (3)

0.5231: COLLINS R-ME

0.5106: FLAKE R-AZ

0.5455: KING I-ME

0.5574: TESTER D-MT

 Closeness (4)

0.5204: BALDWIN D-WI

0.5106: GARDNER R-CO

0.5397: HELLER R-NV

0.5574: HARRIS D-CA

 Closeness (5)

0.5152: LEE R-UT

0.5028: KLOBUCHAR D-MN

0.5312: HARRIS D-CA

0.5514: DURBIN D-IL

 Closeness (6)

0.5152: BOOKER D-NJ

0.5002: KING I-ME

0.5231: KLOBUCHAR D-MN

0.5514: PAUL R-KY

 Closeness (7)

0.51: CORKER R-TN

0.4927: MENENDEZ D-NJ

0.5204: DURBIN D-IL

0.5514: HELLER R-NV

 Closeness (8)

0.51: SCHATZ D-HI

0.4927: HATCH R-UT

0.5178: HASSAN D-NH

0.5455: STABENOW D-MI

 Closeness (9)

0.51: PORTMAN R-OH

0.4902: CARPER D-DE

0.51: BALDWIN D-WI

0.5368: MANCHIN D-WV

 Closeness (10)

0.5075: CASEY D-PA

0.4878: HELLER R-NV

0.5075: KIRK R-IL

0.5368: KIRK R-IL

Betweenness centrality

 Betweenness (1)

0.0552: MANCHIN D-WV

0.0483: MENENDEZ D-NJ

0.0521: LEE R-UT

0.0541: PAUL R-KY

 Betweenness (2)

0.0513: CORKER R-TN

0.046: HELLER R-NV

0.0502: TESTER D-MT

0.0467: CARPER D-DE

 Betweenness (3)

0.0365: CRUZ R-TX

0.0435: FLAKE R-AZ

0.0467: DONNELLY D-IN

0.0415: DURBIN D-IL

 Betweenness (4)

0.0346: HELLER R-NV

0.0428: KING I-ME

0.039: KLOBUCHAR D-MN

0.0335: MORAN R-KS

 Betweenness (5)

0.0339: ENZI R-WY

0.0427: LEE R-UT

0.0331: FLAKE R-AZ

0.0331: MCCASKILL D-MO

 Betweenness (6)

0.0337: HEITKAMP D-ND

0.0415: HEITKAMP D-ND

0.0311: KIRK R-IL

0.0321: TESTER D-MT

 Betweenness (7)

0.0334: KING I-ME

0.0401: TESTER D-MT

0.0293: HELLER R-NV

0.0305: MANCHIN D-WV

 Betweenness (8)

0.0302: LEE R-UT

0.0369: MANCHIN D-WV

0.0292: PAUL R-KY

0.0281: LEE R-UT

 Betweenness (9)

0.0264: BALDWIN D-WI

0.0314: CARPER D-DE

0.0286: SANDERS I-VT

0.028: MCCONNELL R-KY

 Betweenness (10)

0.0262: PAUL R-KY

0.0284: DONNELLY D-IN

0.0286: HEITKAMP D-ND

0.0273: DONNELLY D-IN

Eigenvector centrality

 Eigenvector (1)

0.2016: LEE R-UT

0.2159: MANCHIN D-WV

0.2174: TESTER D-MT

0.22: MCCASKILL D-MO

 Eigenvector (2)

0.1908: MANCHIN D-WV

0.2128: HEITKAMP D-ND

0.1995: KING I-ME

0.2109: CARPER D-DE

 Eigenvector (3)

0.1874: BALDWIN D-WI

0.1926: GARDNER R-CO

0.1801: DONNELLY D-IN

0.1908: HARRIS D-CA

 Eigenvector (4)

0.1873: SCHATZ D-HI

0.1884: KING I-ME

0.1719: HEITKAMP D-ND

0.1852: PAUL R-KY

 Eigenvector (5)

0.1819: COLLINS R-ME

0.1864: FLAKE R-AZ

0.169: CARPER D-DE

0.1766: TESTER D-MT

 Eigenvector (6)

0.1675: SANDERS I-VT

0.1697: HATCH R-UT

0.1677: KIRK R-IL

0.1696: KIRK R-IL

 Eigenvector (7)

0.1671: BOOKER D-NJ

0.1642: ALEXANDER R-TN

0.1643: HELLER R-NV

0.1674: STABENOW D-MI

 Eigenvector (8)

0.1623: CORKER R-TN

0.1642: CARPER D-DE

0.1573: GRAHAM R-SC

0.166: MANCHIN D-WV

 Eigenvector (9)

0.1577: HELLER R-NV

0.1633: LANKFORD R-OK

0.1549: KLOBUCHAR D-MN

0.157: DURBIN D-IL

 Eigenvector (10)

0.1442: PAUL R-KY

0.1603: MENENDEZ D-NJ

0.1536: COLLINS R-ME

0.1566: WARREN D-MA