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Table 6 Fagin’s intersection metric between the proposed and the traditional centrality measures and on considered real-world networks given in Table 1

From: Node-weighted centrality: a new way of centrality hybridization

Instance name

HABC

EABC (\(\alpha =0.5)\)

EABC (\(\alpha =0.75)\)

BC

CC

DC

EC

BC

CC

DC

EC

BC

CC

DC

EC

Chicago Road

0.6487

0.8122

0.6106

0.8187

0.6639

0.7809

0.6286

0.7873

0.6308

0.8073

0.5992

0.816

Chilean Power Grid

0.7007

0.9529

0.6461

0.7418

0.7105

0.9212

0.6553

0.7361

0.6912

0.966

0.6398

0.7416

Euroroad

0.9986

0.5866

0.6477

0.4884

0.9992

0.5869

0.648

0.4888

0.9983

0.5863

0.6477

0.4882

London Metro

0.6801

0.9379

0.6831

0.8843

0.7217

0.8795

0.7013

0.8351

0.6582

0.9546

0.6729

0.8954

Madrid Metro

0.7071

0.9205

0.6645

0.7385

0.749

0.8651

0.6862

0.6978

0.6809

0.9407

0.6542

0.7437

Mexico Metro

0.7546

0.9159

0.6332

0.9014

0.7898

0.8676

0.6409

0.858

0.7289

0.9326

0.618

0.9006

Minnesota Road

0.2845

0.1173

0.3375

0.0239

0.6407

0.2839

0.3661

0.1631

0.3023

0.1223

0.3434

0.0615

Moscow Metro

0.7809

0.9413

0.7758

0.9056

0.7967

0.9193

0.7825

0.8875

0.7615

0.9596

0.7769

0.9083

New York Metro

0.704

0.9081

0.6248

0.7317

0.7949

0.7963

0.6488

0.658

0.7004

0.9022

0.6253

0.7257

Oldenburg Road

0.493

0.8842

0.1815

0.1423

0.7121

0.6117

0.2158

0.1234

0.5207

0.8129

0.1877

0.129

Openflights

0.5825

0.9675

0.7762

0.8194

0.5798

0.9674

0.7753

0.8207

0.5765

0.9632

0.7704

0.8194

Osaka Metro

0.7505

0.9264

0.6979

0.869

0.7758

0.8949

0.7085

0.8427

0.7134

0.958

0.6749

0.8659

p2p-Gnutella08

0.4044

0.926

0.5036

0.8427

0.3999

0.9203

0.4997

0.8474

0.4049

0.9291

0.5057

0.8394

as20000102

0.3204

0.9779

0.4107

0.8947

0.3181

0.9792

0.4085

0.8932

0.3245

0.9823

0.4143

0.8864

Seoul Metro

0.6927

0.9099

0.6274

0.709

0.7945

0.794

0.6263

0.641

0.6883

0.9047

0.6269

0.7098

Shanghai Metro

0.7429

0.8944

0.6196

0.7672

0.7999

0.8264

0.6534

0.7504

0.7165

0.92

0.6016

0.7629

US Air

0.8097

0.9562

0.8614

0.8836

0.8056

0.9541

0.8574

0.8823

0.8026

0.951

0.8538

0.8786

US Power Grid

0.5087

0.8876

0.2427

0.1926

0.5869

0.7553

0.2679

0.1789

0.5025

0.8659

0.2449

0.1949

Paris Metro

0.7242

0.9392

0.6342

0.9106

0.7554

0.8876

0.6523

0.8702

0.7059

0.955

0.6258

0.9207

Tokyo Metro

0.7012

0.932

0.6779

0.8424

0.7305

0.8956

0.69

0.8181

0.6758

0.9439

0.6631

0.843

NRPG data

0.8047

0.9426

0.6834

0.7305

0.8181

0.917

0.694

0.7396

0.7833

0.9572

0.6749

0.7213

Average correlation

0.6569

0.8684

0.5971

0.7066

0.7116

0.8240

0.6098

0.6914

0.6461

0.8721

0.5915

0.7073

Standard deviation

0.1715

0.1903

0.1716

0.2655

0.1480

0.1613

0.1659

0.2452

0.1629

0.1929

0.1671

0.2621