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Table 3 Ranking list of top three central nodes using the proposed hybrid measures and the traditional centrality measures on considered real-world networks given in TableĀ 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
R1 R2 R3 R1 R2 R3 R1 R2 R3 R1 R2 R3 R1 R2 R3 R1 R2 R3 R1 R2 R3
Chicago Road 1156 1157 1147 1156 1157 1147 1156 1157 1147 1156 1157 1147 1156 1157 1147 552 922 10 1156 1147 1150
Chilean Power Grid 178 105 147 178 105 147 178 105 147 178 105 108 178 105 147 108 6 178 108 264 29
Euroroad 402 284 277 402 284 277 402 284 277 402 284 277 401 402 403 284 7 39 7 43 454
London Metro 115 29 12 115 29 12 115 29 12 12 115 180 115 29 214 12 164 305 214 115 219
Madrid Metro 80 162 146 80 162 146 162 80 146 80 146 162 162 80 235 80 15 9 15 54 40
Mexico Metro 26 70 23 26 70 78 70 26 54 26 70 25 70 26 23 26 127 61 26 70 23
Minnesota Road 300 328 280 1821 2069 300 280 328 300 1821 2069 2063 1356 1820 1109 2418 35 32 1927 1930 1987
Moscow Metro 59 71 25 59 71 25 71 59 73 25 74 59 73 71 25 24 59 21 59 25 73
New York Metro 424 191 410 424 191 410 424 191 410 424 191 148 84 424 410 273 228 410 273 228 188
Oldenburg Road 831 714 731 831 714 711 831 714 803 831 714 593 714 731 712 831 1657 1571 1677 1683 1691
Openflights 53 65 57 53 57 65 53 57 65 53 65 1576 53 65 57 53 65 59 53 59 65
Osaka Metro 25 70 95 25 70 95 70 95 25 25 99 70 95 70 25 25 54 42 25 81 54
p2p-Gnutella08 123 367 127 123 367 127 123 127 367 5831 1317 424 123 127 1317 123 127 367 367 123 145
Paris Metro 150 57 235 150 57 235 150 57 235 57 150 106 57 150 235 57 177 246 186 150 235
as20000102 2 10 7 2 10 7 2 10 7 2 7 10 2 10 7 2 10 7 2 10 7
Seoul Metro 220 480 357 220 444 391 220 480 357 220 444 391 220 480 357 254 444 391 103 254 125
Shanghai Metro 136 16 113 136 16 213 136 113 16 16 136 65 136 113 97 16 136 220 16 137 138
Tokyo Metro 150 85 53 150 85 53 85 150 60 150 53 85 150 60 85 150 53 120 150 120 36
US Air 118 261 201 118 201 47 118 201 47 118 8 261 118 261 67 118 261 255 118 261 255
US Power Grid 1378 1365 2685 1378 1365 2685 1378 1365 1678 651 559 1365 1378 1678 2944 2847 602 932 4422 4436 4419
NRPG data 233 235 238 233 235 238 233 235 238 70 235 213 233 238 70 194 65 56 239 213 215