Extracting Backbones from Weighted Complex Networks with Incomplete Information

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static-preview.hindawi.com/articles/aaa/volume-2015/105385/figures/105385.fig.005a.svgz" name="105385.fig.005a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b><span style="font-family:monospace">Lesmis</span>: <svg height="12.4543pt" id="M213" style="vertical-align:-0.1857996pt" version="1.1" viewbox="-0.0498162 -12.2685 52.8844 12.4543" width="52.8844pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><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" id="g190-67"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="588" vert-adv-y="588"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,7.912,0)"><path d="M517 162C503 123 484 88 467 68C445 42 417 34 341 34C291 34 256 34 237 47C219 59 213 81 213 128V317H308C395 317 402 311 415 240H444V431H415C403 364 398 356 307 356H213V584C213 613 215 616 246 616H322C394 616 421 609 435 587C448 566 458 544 467 502L496 506C493 557 488 625 488 650H42V622C120 616 128 612 128 523V125C128 43 120 35 29 28V0H511C520 31 540 125 546 158L517 162Z" id="g190-70"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="568" vert-adv-y="568"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,15.607,0)"><path d="M729 650H468V622C546 615 554 610 554 527V365H213V527C213 610 221 616 297 622V650H38V622C120 616 128 611 128 527V123C128 39 120 34 40 28V0H303V28C221 34 213 40 213 123V322H554V123C554 39 546 34 460 28V0H728V28C647 34 639 39 639 123V527C639 610 647 615 729 622V650Z" id="g190-73"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="766" vert-adv-y="766"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,25.536,0)"><path d="M696 437H516V411C580 402 587 397 574 345C555 271 527 183 505 114H503C461 222 420 328 383 432H357C315 316 278 214 241 118H239C214 195 189 274 165 350C151 396 156 402 216 411V437H9V411C57 405 65 398 83 346C125 226 162 108 199 -11H227C267 100 308 199 346 300C387 195 428 97 468 -11H497C542 124 587 257 617 337C637 392 646 404 696 411V437Z" id="g190-120"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="685" vert-adv-y="685"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,34.817,0)"><path d="M303 0V28C221 34 213 39 213 125V525C213 610 221 616 303 622V650H38V622C120 616 128 610 128 525V125C128 40 120 34 38 28V0H303Z" id="g190-74"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="341" vert-adv-y="341"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,39.587,0)"><path d="M303 0V28C221 34 213 39 213 125V525C213 610 221 616 303 622V650H38V622C120 616 128 610 128 525V125C128 40 120 34 38 28V0H303Z" id="g190-74"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="341" vert-adv-y="341"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,44.224,-5.984)"><path d="M870 650H600L593 618C681 609 684 605 669 516L641 367H261L286 516C302 603 313 610 391 618L398 650H132L123 618C214 610 218 606 200 516L127 130C113 46 107 40 25 32L18 0H290L298 32C204 40 200 42 214 130L250 321H631L596 131C580 47 573 39 484 32L475 0H753L762 32C673 39 668 46 685 130L757 516C772 606 778 610 861 618L870 650Z" id="g50-73"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="882" vert-adv-y="882"></glyph.data></g></svg></td></tr><tr class="fig-image" id="b"><td><object data="https://static-preview.hindawi.com/articles/aaa/volume-2015/105385/figures/105385.fig.005b.svgz" name="105385.fig.005b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b><span style="font-family:monospace">Lesmis</span>: DF</td></tr><tr class="fig-image" id="c"><td><object data="https://static-preview.hindawi.com/articles/aaa/volume-2015/105385/figures/105385.fig.005c.svgz" name="105385.fig.005c" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(c) </b><span style="font-family:monospace">USAir97</span>: <svg height="12.4543pt" id="M214" style="vertical-align:-0.1857996pt" version="1.1" viewbox="-0.0498162 -12.2685 52.8844 12.4543" width="52.8844pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><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" id="g190-67"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="588" vert-adv-y="588"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,7.912,0)"><path d="M517 162C503 123 484 88 467 68C445 42 417 34 341 34C291 34 256 34 237 47C219 59 213 81 213 128V317H308C395 317 402 311 415 240H444V431H415C403 364 398 356 307 356H213V584C213 613 215 616 246 616H322C394 616 421 609 435 587C448 566 458 544 467 502L496 506C493 557 488 625 488 650H42V622C120 616 128 612 128 523V125C128 43 120 35 29 28V0H511C520 31 540 125 546 158L517 162Z" id="g190-70"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="568" vert-adv-y="568"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,15.607,0)"><path d="M729 650H468V622C546 615 554 610 554 527V365H213V527C213 610 221 616 297 622V650H38V622C120 616 128 611 128 527V123C128 39 120 34 40 28V0H303V28C221 34 213 40 213 123V322H554V123C554 39 546 34 460 28V0H728V28C647 34 639 39 639 123V527C639 610 647 615 729 622V650Z" id="g190-73"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="766" vert-adv-y="766"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,25.536,0)"><path d="M696 437H516V411C580 402 587 397 574 345C555 271 527 183 505 114H503C461 222 420 328 383 432H357C315 316 278 214 241 118H239C214 195 189 274 165 350C151 396 156 402 216 411V437H9V411C57 405 65 398 83 346C125 226 162 108 199 -11H227C267 100 308 199 346 300C387 195 428 97 468 -11H497C542 124 587 257 617 337C637 392 646 404 696 411V437Z" id="g190-120"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="685" vert-adv-y="685"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,34.817,0)"><path d="M303 0V28C221 34 213 39 213 125V525C213 610 221 616 303 622V650H38V622C120 616 128 610 128 525V125C128 40 120 34 38 28V0H303Z" id="g190-74"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="341" vert-adv-y="341"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,39.587,0)"><path d="M303 0V28C221 34 213 39 213 125V525C213 610 221 616 303 622V650H38V622C120 616 128 610 128 525V125C128 40 120 34 38 28V0H303Z" id="g190-74"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="341" vert-adv-y="341"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,44.224,-5.984)"><path d="M870 650H600L593 618C681 609 684 605 669 516L641 367H261L286 516C302 603 313 610 391 618L398 650H132L123 618C214 610 218 606 200 516L127 130C113 46 107 40 25 32L18 0H290L298 32C204 40 200 42 214 130L250 321H631L596 131C580 47 573 39 484 32L475 0H753L762 32C673 39 668 46 685 130L757 516C772 606 778 610 861 618L870 650Z" id="g50-73"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="882" vert-adv-y="882"></glyph.data></g></svg></td></tr><tr class="fig-image" id="d"><td><object data="https://static-preview.hindawi.com/articles/aaa/volume-2015/105385/figures/105385.fig.005d.svgz" name="105385.fig.005d" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(d) </b><span style="font-family:monospace">USAir97</span>: DF</td></tr></table>

<div>Comparison in terms of network visualizations.</div>

Abstract and Applied Analysis

fig5

Figure 5

Figure 5: Extracting Backbones from Weighted Complex Networks with Incomplete Information 