Enhancing Controllability Robustness of <svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" id="M1" style="vertical-align:-2.73187pt" height="8.53433pt" version="1.1" viewBox="-0.0498162 -5.80246 7.46902 8.53433" width="7.46902pt">


<g transform="matrix(.0125,0,0,-0.0125,0,0)"><path d="M549 458L539 464L465 428C436 454 396 463 360 463C228 463 72 316 72 147C72 47 132 -10 218 -10C264 -10 321 7 366 42L308 -192L372 -216L382 -211L549 458ZM395 158C358 99 298 61 252 61C187 61 155 106 155 168C155 300 267 392 346 392C384 392 421 370 438 329L395 158Z"/><glyph.data ascent="819" descent="-232" horiz-adv-x="498" vert-adv-y="498"/></g>

</svg>-Snapback Networks through Redirecting Edges

<div class="floats-full-page floats-full-page-other"><h2>Table 1</h2><div class="floats-full-page-caption"><div>Attack methods in simulations.</div></div><div class="floats-full-page-content"><table class="fixed-width table-group" id="tab1"><tr><td><table class="table"><colgroup><col style="width:5.71em" /><col style="width:6.41em" /><col style="width:22.13em" /><col style="width:21.84em" /></colgroup><tr><td class="thead-hr" colspan="4"><hr /></td></tr><tr class="thead"><td class="align_left"> </td><td class="align_center"> </td><td class="align_center">Node-removal</td><td class="align_center">Edge-removal</td></tr><tr><td class="thead-hr" colspan="4"><hr /></td></tr><tr><td class="align_left">Intentional</td><td class="align_center">Betweenness</td><td class="align_center"><span class="nowrap"><svg height="11.9936pt" id="M68" style="vertical-align:-3.2272pt" version="1.1" viewbox="-0.0498162 -8.7664 23.2086 11.9936" width="23.2086pt" 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="M592 498C586 556 582 629 581 675H560C545 656 537 650 510 650H115C87 650 74 652 60 675H40C38 620 33 555 28 495H57C69 539 77 568 89 585C102 607 122 616 205 616H267V123C267 44 259 34 168 28V0H454V28C360 34 352 44 352 123V616H422C498 616 514 608 531 584C542 568 552 543 562 495L592 498Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.021,0)"><path d="M372 352C427 368 507 407 507 502C507 548 486 592 451 616C420 638 376 650 301 650H44V622C124 616 128 610 128 527V123C128 40 122 34 36 28V0H257C336 0 402 12 453 40C512 72 548 124 548 191C548 291 471 335 372 350V352ZM213 362V558C213 591 216 602 226 608C235 614 258 618 282 618C377 618 415 558 415 490C415 406 369 362 260 362H213ZM213 328H258C380 328 450 283 450 181C450 76 377 35 296 34C231 34 213 53 213 125V328Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,15.724,3.132)"><path d="M731 650H485V618C556 614 580 601 585 558C588 530 592 485 592 390V153H589L173 650H22V618C69 614 92 606 112 582C131 558 132 555 132 483V266C132 175 129 128 125 96C120 49 95 36 36 33V0H281V33C212 36 188 50 183 98C180 129 177 175 177 266V510H179L603 -9H638V390C638 483 640 530 644 561C649 602 674 615 731 618V650Z"></path></g></svg>:</span> Remove the node with the largest betweenness</td><td class="align_center"><span class="nowrap"><svg height="11.9479pt" id="M69" style="vertical-align:-3.181499pt" version="1.1" viewbox="-0.0498162 -8.7664 21.6193 11.9479" width="21.6193pt" 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="M592 498C586 556 582 629 581 675H560C545 656 537 650 510 650H115C87 650 74 652 60 675H40C38 620 33 555 28 495H57C69 539 77 568 89 585C102 607 122 616 205 616H267V123C267 44 259 34 168 28V0H454V28C360 34 352 44 352 123V616H422C498 616 514 608 531 584C542 568 552 543 562 495L592 498Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.021,0)"><path d="M372 352C427 368 507 407 507 502C507 548 486 592 451 616C420 638 376 650 301 650H44V622C124 616 128 610 128 527V123C128 40 122 34 36 28V0H257C336 0 402 12 453 40C512 72 548 124 548 191C548 291 471 335 372 350V352ZM213 362V558C213 591 216 602 226 608C235 614 258 618 282 618C377 618 415 558 415 490C415 406 369 362 260 362H213ZM213 328H258C380 328 450 283 450 181C450 76 377 35 296 34C231 34 213 53 213 125V328Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,15.724,3.132)"><path d="M522 166C507 123 488 90 472 71C449 44 419 38 347 38C296 38 261 38 242 51C223 63 217 85 217 132V315H311C398 315 406 310 419 239H453V433H419C406 365 401 358 311 358H217V580C217 609 219 612 251 612H331C400 612 427 604 440 584C453 561 463 541 472 498L506 502C501 558 497 627 497 650H43V618C122 610 130 609 130 520V128C130 46 121 40 30 32V0H521C529 30 552 128 557 162L522 166Z"></path></g></svg>:</span> Remove the edge with the largest betweenness</td></tr><tr><td class="align_left"> </td><td class="align_center">Degree</td><td class="align_center"><span class="nowrap"><svg height="11.9936pt" id="M70" style="vertical-align:-3.2272pt" version="1.1" viewbox="-0.0498162 -8.7664 25.1268 11.9936" width="25.1268pt" 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="M592 498C586 556 582 629 581 675H560C545 656 537 650 510 650H115C87 650 74 652 60 675H40C38 620 33 555 28 495H57C69 539 77 568 89 585C102 607 122 616 205 616H267V123C267 44 259 34 168 28V0H454V28C360 34 352 44 352 123V616H422C498 616 514 608 531 584C542 568 552 543 562 495L592 498Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.021,0)"><path d="M43 650V622C120 616 128 612 128 526V124C128 39 120 33 34 27V0H270C392 0 492 25 567 83C643 141 690 230 690 350C690 444 655 517 605 565C543 625 450 650 323 650H43ZM213 547C213 587 217 598 226 604C236 612 262 617 304 617C371 617 429 604 474 576C554 529 592 439 592 336C592 176 505 36 319 36C246 36 213 55 213 131V547Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,17.642,3.132)"><path d="M731 650H485V618C556 614 580 601 585 558C588 530 592 485 592 390V153H589L173 650H22V618C69 614 92 606 112 582C131 558 132 555 132 483V266C132 175 129 128 125 96C120 49 95 36 36 33V0H281V33C212 36 188 50 183 98C180 129 177 175 177 266V510H179L603 -9H638V390C638 483 640 530 644 561C649 602 674 615 731 618V650Z"></path></g></svg>:</span> Remove the node with the largest outdegree</td><td class="align_center"><span class="nowrap"><svg height="11.9479pt" id="M71" style="vertical-align:-3.181499pt" version="1.1" viewbox="-0.0498162 -8.7664 23.5375 11.9479" width="23.5375pt" 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="M592 498C586 556 582 629 581 675H560C545 656 537 650 510 650H115C87 650 74 652 60 675H40C38 620 33 555 28 495H57C69 539 77 568 89 585C102 607 122 616 205 616H267V123C267 44 259 34 168 28V0H454V28C360 34 352 44 352 123V616H422C498 616 514 608 531 584C542 568 552 543 562 495L592 498Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.021,0)"><path d="M43 650V622C120 616 128 612 128 526V124C128 39 120 33 34 27V0H270C392 0 492 25 567 83C643 141 690 230 690 350C690 444 655 517 605 565C543 625 450 650 323 650H43ZM213 547C213 587 217 598 226 604C236 612 262 617 304 617C371 617 429 604 474 576C554 529 592 439 592 336C592 176 505 36 319 36C246 36 213 55 213 131V547Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,17.642,3.132)"><path d="M522 166C507 123 488 90 472 71C449 44 419 38 347 38C296 38 261 38 242 51C223 63 217 85 217 132V315H311C398 315 406 310 419 239H453V433H419C406 365 401 358 311 358H217V580C217 609 219 612 251 612H331C400 612 427 604 440 584C453 561 463 541 472 498L506 502C501 558 497 627 497 650H43V618C122 610 130 609 130 520V128C130 46 121 40 30 32V0H521C529 30 552 128 557 162L522 166Z"></path></g></svg>:</span> Remove the edge with the largest edge degree</td></tr><tr><td class="align_left" colspan="4"><hr /></td></tr><tr><td class="align_center" colspan="2"> Random</td><td class="align_center"><span class="nowrap"><svg height="11.6151pt" id="M72" style="vertical-align:-3.227119pt" version="1.1" viewbox="-0.0498162 -8.38798 15.5882 11.6151" width="15.5882pt" 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="M631 18C609 24 585 35 559 65C534 91 514 117 478 169C448 214 406 281 389 313C462 346 516 399 516 485C516 545 490 590 449 616C412 641 363 650 290 650H42V622C120 615 128 612 128 527V125C128 40 120 34 38 28V0H300V28C221 34 212 40 212 125V284H244C295 284 312 272 329 244C359 195 395 133 430 84C475 19 516 -3 592 -7C603 -8 615 -8 627 -8L631 18ZM212 316V563C212 591 215 602 223 607C231 613 248 617 277 617C352 617 423 577 423 469C423 415 407 375 368 345C343 324 310 316 260 316H212Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.073,3.132)"><path d="M731 650H485V618C556 614 580 601 585 558C588 530 592 485 592 390V153H589L173 650H22V618C69 614 92 606 112 582C131 558 132 555 132 483V266C132 175 129 128 125 96C120 49 95 36 36 33V0H281V33C212 36 188 50 183 98C180 129 177 175 177 266V510H179L603 -9H638V390C638 483 640 530 644 561C649 602 674 615 731 618V650Z"></path></g></svg>:</span> Remove a node randomly</td><td class="align_center"><span class="nowrap"><svg height="11.5695pt" id="M73" style="vertical-align:-3.18152pt" version="1.1" viewbox="-0.0498162 -8.38798 13.9988 11.5695" width="13.9988pt" 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="M631 18C609 24 585 35 559 65C534 91 514 117 478 169C448 214 406 281 389 313C462 346 516 399 516 485C516 545 490 590 449 616C412 641 363 650 290 650H42V622C120 615 128 612 128 527V125C128 40 120 34 38 28V0H300V28C221 34 212 40 212 125V284H244C295 284 312 272 329 244C359 195 395 133 430 84C475 19 516 -3 592 -7C603 -8 615 -8 627 -8L631 18ZM212 316V563C212 591 215 602 223 607C231 613 248 617 277 617C352 617 423 577 423 469C423 415 407 375 368 345C343 324 310 316 260 316H212Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.073,3.132)"><path d="M522 166C507 123 488 90 472 71C449 44 419 38 347 38C296 38 261 38 242 51C223 63 217 85 217 132V315H311C398 315 406 310 419 239H453V433H419C406 365 401 358 311 358H217V580C217 609 219 612 251 612H331C400 612 427 604 440 584C453 561 463 541 472 498L506 502C501 558 497 627 497 650H43V618C122 610 130 609 130 520V128C130 46 121 40 30 32V0H521C529 30 552 128 557 162L522 166Z"></path></g></svg>:</span> Remove an edge randomly</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr" /></td></tr></table></td></tr></table></div></div>

Table 1 | Enhancing Controllability Robustness of <svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" id="M1" style="vertical-align:-2.73187pt" height="8.53433pt" version="1.1" viewBox="-0.0498162 -5.80246 7.46902 8.53433" width="7.46902pt">


<g transform="matrix(.0125,0,0,-0.0125,0,0)"><path d="M549 458L539 464L465 428C436 454 396 463 360 463C228 463 72 316 72 147C72 47 132 -10 218 -10C264 -10 321 7 366 42L308 -192L372 -216L382 -211L549 458ZM395 158C358 99 298 61 252 61C187 61 155 106 155 168C155 300 267 392 346 392C384 392 421 370 438 329L395 158Z"/><glyph.data ascent="819" descent="-232" horiz-adv-x="498" vert-adv-y="498"/></g>

</svg>-Snapback Networks through Redirecting Edges

title

Table 1: Enhancing Controllability Robustness of <svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" id="M1" style="vertical-align:-2.73187pt" height="8.53433pt" version="1.1" viewBox="-0.0498162 -5.80246 7.46902 8.53433" width="7.46902pt">


<g transform="matrix(.0125,0,0,-0.0125,0,0)"><path d="M549 458L539 464L465 428C436 454 396 463 360 463C228 463 72 316 72 147C72 47 132 -10 218 -10C264 -10 321 7 366 42L308 -192L372 -216L382 -211L549 458ZM395 158C358 99 298 61 252 61C187 61 155 106 155 168C155 300 267 392 346 392C384 392 421 370 438 329L395 158Z"/><glyph.data ascent="819" descent="-232" horiz-adv-x="498" vert-adv-y="498"/></g>

</svg>-Snapback Networks through Redirecting Edges

description

Table 1 | Enhancing Controllability Robustness of 




-Snapback Networks through Redirecting Edges

Table 1

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Enhancing Controllability Robustness of -Snapback Networks through Redirecting Edges

Table 1