Novel Node Centrality-Based Efficient Empirical Robustness Assessment for Directed Network

<div><svg height="16.2709pt" id="M216" style="vertical-align:-4.679501pt" version="1.1" viewbox="-0.0498162 -11.5914 64.4199 16.2709" width="64.4199pt" 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="M238 681C243 705 239 712 230 712C217 712 156 682 75 674L70 648H105C148 648 153 641 144 598L39 110C18 11 35 -12 55 -12C90 -12 166 36 221 103L205 125C174 93 130 65 118 65C112 65 108 68 114 96L238 681Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,3.498,-5.741)"><path d="M556 236V289H56V236H556Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.058,-5.741)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g><g transform="matrix(.013,0,0,-0.013,14.026,0)"><path d="M717 427H488V399C559 390 569 378 549 331C530 287 513 253 489 216C425 282 354 343 321 371C360 397 383 416 402 432C423 450 444 479 444 520C444 600 377 658 296 658C208 658 132 590 132 500C132 446 159 403 204 361C119 300 54 260 54 167C54 80 125 -14 251 -14C323 -14 389 22 461 118C494 84 536 37 548 23C560 10 615 -13 670 -18L677 -9C647 49 556 150 514 191C549 244 573 285 601 324C634 373 647 391 717 399V427ZM285 624C335 624 369 576 369 519C369 465 342 426 295 391C235 437 204 472 204 524C204 584 239 624 285 624ZM278 54C212 54 139 100 139 196C139 245 164 292 230 339C321 265 385 204 438 145C405 99 345 54 278 54Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.347,0)"><path d="M645 631C614 643 545 666 457 666C215 666 23 519 23 283C23 90 158 -16 337 -16C412 -16 489 2 522 10C543 39 590 127 606 167L580 181C519 89 459 18 348 18C201 18 122 136 122 287C122 464 244 632 435 632C544 632 602 595 608 472L639 475C643 526 645 581 645 631Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,31.966,3.132)"><path d="M722 297H451L442 267C561 257 561 253 547 182L531 98C521 44 465 24 390 24C228 24 130 134 130 296C130 482 252 628 465 628C592 628 657 579 656 458L692 461C695 540 699 605 702 631C664 642 590 667 492 667C203 667 24 502 24 285C24 93 170 -17 368 -17C464 -17 543 11 617 28C613 43 612 68 620 106L635 182C649 255 652 258 716 268L722 297Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,38.272,3.132)"><path d="M556 331V384H55V331H556ZM556 140V193H55V140H556Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,43.832,3.132)"><path d="M309 -142C211 -61 151 99 151 271S210 601 309 683L288 710C141 611 75 451 75 272V271C75 90 141 -72 288 -169L309 -142Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,47.09,3.132)"><path d="M735 650H491L482 618L516 614C568 608 571 595 541 535L299 115H297L196 559C187 600 195 608 238 614L265 618L275 650H26L18 618C79 611 98 605 115 527L234 -9H272C389 197 542 449 591 523C647 608 656 612 726 618L735 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,52.542,3.132)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,54.699,3.132)"><path d="M615 650H141L132 618C223 612 227 607 212 526L136 123C122 42 112 38 27 32L18 0H522C539 33 580 135 592 166L558 179C536 139 512 100 486 75C454 48 420 41 345 41C287 41 252 42 237 55C221 68 220 100 231 158L261 316H357C455 316 455 309 455 235H489L529 437H494C468 366 460 360 369 360H269L305 565C315 609 316 611 357 611H450C525 611 535 599 548 578C559 556 561 526 560 482L595 486L615 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,60.368,3.132)"><path d="M283 271C283 451 220 610 70 710L48 683C146 603 207 443 207 271S149 -59 48 -142L70 -169C220 -67 283 90 283 271Z"></path></g></svg> result of Facebook (<i>X</i>-axis logarithmic coordinate).</div>

Complexity

fig20

Figure 20

Figure 20: Novel Node Centrality-Based Efficient Empirical Robustness Assessment for Directed Network 