The Local Triangle Structure Centrality Method to Rank Nodes in Networks

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/complexity/volume-2019/9057194/figures/9057194.fig.004a.svgz" name="9057194.fig.004a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>The top 10 nodes of Karate</td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/complexity/volume-2019/9057194/figures/9057194.fig.004b.svgz" name="9057194.fig.004b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>The top 10% nodes of Karate</td></tr><tr class="fig-image" id="c"><td><object data="https://static.hindawi.com/articles/complexity/volume-2019/9057194/figures/9057194.fig.004c.svgz" name="9057194.fig.004c" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(c) </b>The top 50% nodes of Karate</td></tr><tr class="fig-image" id="d"><td><object data="https://static.hindawi.com/articles/complexity/volume-2019/9057194/figures/9057194.fig.004d.svgz" name="9057194.fig.004d" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(d) </b>The top 10 nodes of Polbook</td></tr><tr class="fig-image" id="e"><td><object data="https://static.hindawi.com/articles/complexity/volume-2019/9057194/figures/9057194.fig.004e.svgz" name="9057194.fig.004e" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(e) </b>The top 10% nodes of Polbook</td></tr><tr class="fig-image" id="f"><td><object data="https://static.hindawi.com/articles/complexity/volume-2019/9057194/figures/9057194.fig.004f.svgz" name="9057194.fig.004f" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(f) </b>The top 50% nodes of Polbook</td></tr><tr class="fig-image" id="g"><td><object data="https://static.hindawi.com/articles/complexity/volume-2019/9057194/figures/9057194.fig.004g.svgz" name="9057194.fig.004g" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(g) </b>The top 10 nodes of Netscience</td></tr><tr class="fig-image" id="h"><td><object data="https://static.hindawi.com/articles/complexity/volume-2019/9057194/figures/9057194.fig.004h.svgz" name="9057194.fig.004h" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(h) </b>The top 10% nodes of Netscience</td></tr><tr class="fig-image" id="i"><td><object data="https://static.hindawi.com/articles/complexity/volume-2019/9057194/figures/9057194.fig.004i.svgz" name="9057194.fig.004i" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(i) </b>The top 50% nodes of Netscience</td></tr></table>

<div>The ranking similarity <svg height="11.5564pt" id="M278" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 24.2659 11.5564" width="24.2659pt" 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="M584 650H137L131 622C214 614 217 612 200 521L125 127C109 41 101 35 23 28L17 0H288L294 28C201 35 193 42 209 128L242 309H348C440 309 442 300 443 226H471L510 422H482C452 354 449 348 357 348H251L295 575C302 609 304 615 338 615H426C502 615 517 604 526 581C534 560 536 524 537 492L565 494C574 554 583 631 584 650Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.895,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,12.393,0)"><path d="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z"></path></g><g transform="matrix(.013,0,0,-0.013,19.578,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg> for the top <svg height="8.68572pt" id="M279" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 7.31558 8.68572" width="7.31558pt" 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="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z"></path></g></svg> nodes of ranks offered by eight evaluating indexes with the SIR model on Karate, Polbook, and Netscience networks, respectively, where <span class="nowrap"><svg height="10.2124pt" id="M280" style="vertical-align:-1.576501pt" version="1.1" viewbox="-0.0498162 -8.6359 89.8574 10.2124" width="89.8574pt" 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="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.817,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,22.08,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,28.32,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,34.56,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,39.703,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,45.943,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,52.287,0)"><path d="M594 629L561 652L159 -9L190 -32L594 629ZM194 635C92 635 49 534 49 453C49 374 92 272 193 272C295 272 338 374 338 454S295 635 194 635ZM193 605C257 605 265 504 265 453C265 405 257 302 194 302C133 302 122 403 122 454S133 605 193 605ZM567 351C465 351 421 250 421 169C421 90 465 -12 566 -12S710 90 710 170S667 351 567 351ZM566 322C628 322 637 221 637 169C637 121 628 18 567 18S494 119 494 170C494 223 506 322 566 322Z"></path></g><g transform="matrix(.013,0,0,-0.013,62.115,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,67.258,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z"></path></g><g transform="matrix(.013,0,0,-0.013,73.499,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,79.785,0)"><path d="M594 629L561 652L159 -9L190 -32L594 629ZM194 635C92 635 49 534 49 453C49 374 92 272 193 272C295 272 338 374 338 454S295 635 194 635ZM193 605C257 605 265 504 265 453C265 405 257 302 194 302C133 302 122 403 122 454S133 605 193 605ZM567 351C465 351 421 250 421 169C421 90 465 -12 566 -12S710 90 710 170S667 351 567 351ZM566 322C628 322 637 221 637 169C637 121 628 18 567 18S494 119 494 170C494 223 506 322 566 322Z"></path></g></svg>.</span></div>

Complexity

fig4

Figure 4

Figure 4: The Local Triangle Structure Centrality Method to Rank Nodes in Networks 