Ranking Spreaders in Complex Networks Based on the Most Influential Neighbors

<table class="fixed-width table-group" id="tab4"><tr><td><table class="table"><colgroup><col style="width:5.14em"/><col style="width:4.95em"/><col style="width:4.82em"/><col style="width:4.86em"/><col style="width:6.21em"/></colgroup><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left">Networks</td><td class="align_center"><span style="width: 47.9363ptpx;"><svg height="11.6804pt" id="M162" style="vertical-align:-2.39207pt" version="1.1" viewbox="-0.0498162 -9.28833 47.9363 11.6804" width="47.9363pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,.241)"><path d="M360 -163L167 270L360 703H298L106 273V267L298 -163H360Z" id="g113-61"></path></g><g transform="matrix(.013,0,0,-0.013,5.389,0)"><path d="M515 461L483 468C463 439 452 438 425 438C350 438 285 442 225 442C87 442 40 359 21 322L50 298C93 355 138 365 217 360C197 286 173 196 152 92C149 77 147 63 147 52C147 5 171 -12 199 -12C273 -12 353 56 385 103L367 134C341 107 305 83 289 83C279 83 274 97 283 147C292 198 312 290 329 353C358 352 385 350 408 350C433 350 458 351 471 356C479 369 499 415 515 461Z" id="g5-241"></path></g><g transform="matrix(.013,0,0,-0.013,12.253,.241)"><path d="M307 267V273L115 703H53L246 270L53 -163H115L307 267Z" id="g113-63"></path></g><g transform="matrix(.013,0,0,-0.013,19.821,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path></g><g transform="matrix(.013,0,0,-0.013,24.336,0)"><path d="M41 650V615C111 608 121 602 121 516V134C121 48 111 42 32 35V0H289C413 0 518 27 592 83C668 141 717 229 717 351C717 446 678 517 628 564C564 625 467 650 341 650H41ZM255 540C255 569 257 586 265 595C272 602 292 609 328 609C397 609 450 589 491 547C537 502 566 426 566 331C566 152 474 43 340 43C270 43 255 68 255 140V540Z" id="g13-66"></path></g><g transform="matrix(.013,0,0,-0.013,34.464,0)"><path d="M625 186C574 85 512 32 429 32C293 32 194 153 194 337C194 485 274 621 419 621C496 621 573 586 606 468L643 475C636 537 629 583 620 638C593 644 519 665 438 665C199 665 42 523 42 317C42 158 152 -15 418 -15C486 -15 578 5 604 11C621 46 647 122 660 171L625 186Z" id="g13-65"></path></g><g transform="matrix(.013,0,0,-0.013,43.252,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path></g></svg></span></td><td class="align_center"><span style="width: 46.1747ptpx;"><svg height="11.6804pt" id="M163" style="vertical-align:-2.39207pt" version="1.1" viewbox="-0.0498162 -9.28833 46.1747 11.6804" width="46.1747pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,.241)"><path d="M360 -163L167 270L360 703H298L106 273V267L298 -163H360Z" id="g113-61"></path></g><g transform="matrix(.013,0,0,-0.013,5.389,0)"><path d="M515 461L483 468C463 439 452 438 425 438C350 438 285 442 225 442C87 442 40 359 21 322L50 298C93 355 138 365 217 360C197 286 173 196 152 92C149 77 147 63 147 52C147 5 171 -12 199 -12C273 -12 353 56 385 103L367 134C341 107 305 83 289 83C279 83 274 97 283 147C292 198 312 290 329 353C358 352 385 350 408 350C433 350 458 351 471 356C479 369 499 415 515 461Z" id="g5-241"></path></g><g transform="matrix(.013,0,0,-0.013,12.253,.241)"><path d="M307 267V273L115 703H53L246 270L53 -163H115L307 267Z" id="g113-63"></path></g><g transform="matrix(.013,0,0,-0.013,19.821,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path></g><g transform="matrix(.013,0,0,-0.013,24.336,0)"><path d="M401 353C473 367 557 406 557 502C557 551 535 592 498 616C460 640 410 650 333 650H41V615C112 608 121 602 121 516V134C121 49 112 42 35 35V0H289C372 0 449 14 500 43C556 74 593 126 593 193C593 288 517 335 401 349V353ZM253 363V553C253 574 255 589 262 596C268 602 284 609 307 609C361 609 415 575 415 484C415 401 372 363 276 363H253ZM253 323H273C386 323 445 276 445 182C445 84 382 43 326 42C273 41 253 62 253 136V323Z" id="g13-64"></path></g><g transform="matrix(.013,0,0,-0.013,32.708,0)"><path d="M625 186C574 85 512 32 429 32C293 32 194 153 194 337C194 485 274 621 419 621C496 621 573 586 606 468L643 475C636 537 629 583 620 638C593 644 519 665 438 665C199 665 42 523 42 317C42 158 152 -15 418 -15C486 -15 578 5 604 11C621 46 647 122 660 171L625 186Z" id="g13-65"></path></g><g transform="matrix(.013,0,0,-0.013,41.496,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path></g></svg></span></td><td class="align_center"><span style="width: 46.7358ptpx;"><svg height="11.6804pt" id="M164" style="vertical-align:-2.39207pt" version="1.1" viewbox="-0.0498162 -9.28833 46.7358 11.6804" width="46.7358pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,.241)"><path d="M360 -163L167 270L360 703H298L106 273V267L298 -163H360Z" id="g113-61"></path></g><g transform="matrix(.013,0,0,-0.013,5.389,0)"><path d="M515 461L483 468C463 439 452 438 425 438C350 438 285 442 225 442C87 442 40 359 21 322L50 298C93 355 138 365 217 360C197 286 173 196 152 92C149 77 147 63 147 52C147 5 171 -12 199 -12C273 -12 353 56 385 103L367 134C341 107 305 83 289 83C279 83 274 97 283 147C292 198 312 290 329 353C358 352 385 350 408 350C433 350 458 351 471 356C479 369 499 415 515 461Z" id="g5-241"></path></g><g transform="matrix(.013,0,0,-0.013,12.253,.241)"><path d="M307 267V273L115 703H53L246 270L53 -163H115L307 267Z" id="g113-63"></path></g><g transform="matrix(.013,0,0,-0.013,19.821,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path></g><g transform="matrix(.013,0,0,-0.013,24.336,0)"><path d="M625 186C574 85 512 32 429 32C293 32 194 153 194 337C194 485 274 621 419 621C496 621 573 586 606 468L643 475C636 537 629 583 620 638C593 644 519 665 438 665C199 665 42 523 42 317C42 158 152 -15 418 -15C486 -15 578 5 604 11C621 46 647 122 660 171L625 186Z" id="g13-65"></path></g><g transform="matrix(.013,0,0,-0.013,33.267,0)"><path d="M625 186C574 85 512 32 429 32C293 32 194 153 194 337C194 485 274 621 419 621C496 621 573 586 606 468L643 475C636 537 629 583 620 638C593 644 519 665 438 665C199 665 42 523 42 317C42 158 152 -15 418 -15C486 -15 578 5 604 11C621 46 647 122 660 171L625 186Z" id="g13-65"></path></g><g transform="matrix(.013,0,0,-0.013,42.055,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path></g></svg></span></td><td class="align_center"><span style="width: 64.2995ptpx;"><svg height="11.6804pt" id="M165" style="vertical-align:-2.39207pt" version="1.1" viewbox="-0.0498162 -9.28833 64.2995 11.6804" width="64.2995pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,.241)"><path d="M360 -163L167 270L360 703H298L106 273V267L298 -163H360Z" id="g113-61"></path></g><g transform="matrix(.013,0,0,-0.013,5.389,0)"><path d="M515 461L483 468C463 439 452 438 425 438C350 438 285 442 225 442C87 442 40 359 21 322L50 298C93 355 138 365 217 360C197 286 173 196 152 92C149 77 147 63 147 52C147 5 171 -12 199 -12C273 -12 353 56 385 103L367 134C341 107 305 83 289 83C279 83 274 97 283 147C292 198 312 290 329 353C358 352 385 350 408 350C433 350 458 351 471 356C479 369 499 415 515 461Z" id="g5-241"></path></g><g transform="matrix(.013,0,0,-0.013,12.253,.241)"><path d="M307 267V273L115 703H53L246 270L53 -163H115L307 267Z" id="g113-63"></path></g><g transform="matrix(.013,0,0,-0.013,19.821,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path></g><g transform="matrix(.013,0,0,-0.013,24.336,0)"><path d="M860 0V35C782 43 777 50 775 142L766 516C764 599 768 607 848 615V650H646L450 212L258 650H51V615C137 607 144 593 136 480L120 282C112 177 105 124 99 93C92 57 74 40 17 35V0H258V35C191 41 172 50 168 95C164 126 163 173 168 256L180 517H184L388 7H416L637 527H642L644 142C644 50 639 43 564 35V0H860Z" id="g13-75"></path></g><g transform="matrix(.013,0,0,-0.013,35.88,0)"><path d="M338 0V35C263 42 255 49 255 133V516C255 602 263 608 338 615V650H37V615C112 608 121 602 121 516V133C121 49 112 42 37 35V0H338Z" id="g13-71"></path></g><g transform="matrix(.013,0,0,-0.013,40.794,0)"><path d="M724 650H480V616C554 612 574 595 579 552C582 523 587 476 587 387V211H584L201 650H16V616C59 612 81 604 100 580S120 538 120 472V264C120 176 114 131 110 98C106 55 83 39 27 35V0H272V35C198 38 181 57 176 101C173 131 168 176 168 264V488H171L587 -10H635V387C635 476 641 523 644 554C649 599 670 613 724 616V650Z" id="g13-76"></path></g><g transform="matrix(.013,0,0,-0.013,50.414,0)"><path d="M699 0V35C659 41 632 57 591 109C519 200 445 301 381 397C426 443 468 491 527 545C582 597 623 609 685 615V650H425V615L443 613C490 607 492 592 468 561C435 516 395 467 328 399C298 368 273 352 252 346V516C252 602 260 608 331 615V650H37V615C112 608 121 602 121 516V134C121 48 111 42 39 35V0H338V35C261 42 252 48 252 134V314C267 316 280 310 301 280C372 176 455 59 498 0H699Z" id="g13-73"></path></g><g transform="matrix(.013,0,0,-0.013,59.553,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left">BA</td><td class="align_center">0.3052</td><td class="align_center">0.3833</td><td class="align_center">0.7123</td><td class="align_center">0.7354</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div><svg height="11.5564pt" id="M160" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 29.7464 11.5564" width="29.7464pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M360 -163L167 270L360 703H298L106 273V267L298 -163H360Z" id="g113-61"></path></g><g transform="matrix(.013,0,0,-0.013,5.369,0)"><path d="M515 461L483 468C463 439 452 438 425 438C350 438 285 442 225 442C87 442 40 359 21 322L50 298C93 355 138 365 217 360C197 286 173 196 152 92C149 77 147 63 147 52C147 5 171 -12 199 -12C273 -12 353 56 385 103L367 134C341 107 305 83 289 83C279 83 274 97 283 147C292 198 312 290 329 353C358 352 385 350 408 350C433 350 458 351 471 356C479 369 499 415 515 461Z" id="g5-241"></path></g><g transform="matrix(.013,0,0,-0.013,12.233,0)"><path d="M307 267V273L115 703H53L246 270L53 -163H115L307 267Z" id="g113-63"></path></g><g transform="matrix(.013,0,0,-0.013,17.622,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path></g><g transform="matrix(.013,0,0,-0.013,22.137,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path></g><g transform="matrix(.013,0,0,-0.013,25.101,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path></g></svg> is the average value of the Kendall’s tau <svg height="6.1673pt" id="M161" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 6.40217 6.1673" width="6.40217pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M471 456L444 459C426 433 414 430 388 430C324 430 270 434 216 434C103 434 51 374 23 338L43 317C96 366 146 380 221 375L154 109C149 86 147 68 147 52C147 4 168 -12 197 -12C240 -12 291 25 334 71L320 96C295 75 268 58 252 58C238 58 227 79 238 138C251 211 272 296 292 372C310 372 332 368 350 368C391 368 421 369 434 371C444 388 455 413 471 456Z" id="g113-241"></path></g></svg> under different infection rates for the BA network.</div>

Discrete Dynamics in Nature and Society

tab4

Table 4

Table 4: Ranking Spreaders in Complex Networks Based on the Most Influential Neighbors 