Azimuthal Anisotropy in High-Energy Nuclear Collision: An Approach Based on Complex Network Analysis

<div>(a) <svg height="11.5564pt" id="M200" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 23.744 11.5564" width="23.744pt" 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="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z" id="g113-81"></path></g><g transform="matrix(.013,0,0,-0.013,8.026,0)"><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,-0.013,12.524,0)"><path d="M480 416C480 431 465 448 438 448C388 448 312 383 252 330C217 299 188 273 155 237H153L257 680C262 700 263 712 253 712C240 712 183 684 97 674L92 648L126 647C166 646 172 645 163 606L23 -6L29 -12C51 -5 77 2 107 8C115 62 130 128 142 180C153 193 179 220 204 241C231 170 259 106 288 54C317 0 336 -12 358 -12C381 -12 423 2 477 80L460 100C434 74 408 54 398 54C385 54 374 65 351 107C326 154 282 241 263 299C296 332 351 377 403 377C424 377 436 372 445 368C449 366 456 368 462 375C472 386 480 402 480 416Z" id="g113-108"></path></g><g transform="matrix(.013,0,0,-0.013,19.063,0)"><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> versus <svg height="9.49473pt" id="M201" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 6.66314 9.49473" width="6.66314pt" 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="M480 416C480 431 465 448 438 448C388 448 312 383 252 330C217 299 188 273 155 237H153L257 680C262 700 263 712 253 712C240 712 183 684 97 674L92 648L126 647C166 646 172 645 163 606L23 -6L29 -12C51 -5 77 2 107 8C115 62 130 128 142 180C153 193 179 220 204 241C231 170 259 106 288 54C317 0 336 -12 358 -12C381 -12 423 2 477 80L460 100C434 74 408 54 398 54C385 54 374 65 351 107C326 154 282 241 263 299C296 332 351 377 403 377C424 377 436 372 445 368C449 366 456 368 462 375C472 386 480 402 480 416Z" id="g113-108"></path></g></svg> plot for a cluster (b) <svg height="13.1562pt" id="M202" style="vertical-align:-3.86787pt" version="1.1" viewbox="-0.0498162 -9.28833 53.7571 13.1562" width="53.7571pt" 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 0V26C174 32 166 38 166 104V712C132 700 70 683 18 677V653C81 647 87 645 87 577V104C87 38 78 32 15 26V0H238Z" id="g121-106"></path></g><g transform="matrix(.013,0,0,-0.013,3.289,0)"><path d="M257 449C165 449 37 374 37 209C37 98 119 -12 256 -12C355 -12 473 65 473 226C473 349 381 449 257 449ZM244 416C333 416 380 320 380 204C380 67 329 21 267 21C184 21 130 115 130 241C130 354 184 416 244 416Z" id="g121-109"></path></g><g transform="matrix(.013,0,0,-0.013,9.919,0)"><path d="M463 437C426 431 375 425 327 422C297 440 264 449 231 449H230C153 449 51 396 51 283C51 215 94 168 139 149C123 129 91 103 51 88C50 78 53 60 62 46C75 25 100 2 136 -9C112 -28 73 -59 53 -79C38 -94 29 -113 29 -135C30 -192 91 -257 203 -257C336 -257 452 -160 452 -59C452 39 371 59 309 59C275 59 240 58 203 58C158 58 140 77 140 96C140 110 157 129 170 138C186 135 205 133 221 133C306 133 396 185 396 293C396 328 384 360 366 381L423 378C439 387 459 413 468 429L463 437ZM219 418C277 418 314 362 314 284C314 205 275 166 231 165C176 165 137 221 137 299C137 376 177 418 219 418ZM241 -11C285 -11 314 -14 339 -24C367 -36 384 -61 384 -95C384 -157 335 -206 240 -206C166 -206 108 -165 108 -110C108 -82 128 -54 154 -32C172 -17 195 -11 241 -11Z" id="g121-101"></path></g><g transform="matrix(.0091,0,0,-0.0091,16.063,3.818)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path></g><g transform="matrix(.013,0,0,-0.013,21.01,0)"><path d="M290 -163V-135C183 -126 181 -122 181 -44V583C181 662 184 666 290 675V703H120V-163H290Z" id="g113-92"></path></g><g transform="matrix(.013,0,0,-0.013,25.494,0)"><path d="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z" id="g113-81"></path></g><g transform="matrix(.013,0,0,-0.013,33.521,0)"><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,-0.013,38.019,0)"><path d="M480 416C480 431 465 448 438 448C388 448 312 383 252 330C217 299 188 273 155 237H153L257 680C262 700 263 712 253 712C240 712 183 684 97 674L92 648L126 647C166 646 172 645 163 606L23 -6L29 -12C51 -5 77 2 107 8C115 62 130 128 142 180C153 193 179 220 204 241C231 170 259 106 288 54C317 0 336 -12 358 -12C381 -12 423 2 477 80L460 100C434 74 408 54 398 54C385 54 374 65 351 107C326 154 282 241 263 299C296 332 351 377 403 377C424 377 436 372 445 368C449 366 456 368 462 375C472 386 480 402 480 416Z" id="g113-108"></path></g><g transform="matrix(.013,0,0,-0.013,44.558,0)"><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><g transform="matrix(.013,0,0,-0.013,49.056,0)"><path d="M226 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H226Z" id="g113-94"></path></g></svg> versus <svg height="13.1562pt" id="M203" style="vertical-align:-3.86787pt" version="1.1" viewbox="-0.0498162 -9.28833 48.3157 13.1562" width="48.3157pt" 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 0V26C174 32 166 38 166 104V712C132 700 70 683 18 677V653C81 647 87 645 87 577V104C87 38 78 32 15 26V0H238Z" id="g121-106"></path></g><g transform="matrix(.013,0,0,-0.013,3.289,0)"><path d="M257 449C165 449 37 374 37 209C37 98 119 -12 256 -12C355 -12 473 65 473 226C473 349 381 449 257 449ZM244 416C333 416 380 320 380 204C380 67 329 21 267 21C184 21 130 115 130 241C130 354 184 416 244 416Z" id="g121-109"></path></g><g transform="matrix(.013,0,0,-0.013,9.919,0)"><path d="M463 437C426 431 375 425 327 422C297 440 264 449 231 449H230C153 449 51 396 51 283C51 215 94 168 139 149C123 129 91 103 51 88C50 78 53 60 62 46C75 25 100 2 136 -9C112 -28 73 -59 53 -79C38 -94 29 -113 29 -135C30 -192 91 -257 203 -257C336 -257 452 -160 452 -59C452 39 371 59 309 59C275 59 240 58 203 58C158 58 140 77 140 96C140 110 157 129 170 138C186 135 205 133 221 133C306 133 396 185 396 293C396 328 384 360 366 381L423 378C439 387 459 413 468 429L463 437ZM219 418C277 418 314 362 314 284C314 205 275 166 231 165C176 165 137 221 137 299C137 376 177 418 219 418ZM241 -11C285 -11 314 -14 339 -24C367 -36 384 -61 384 -95C384 -157 335 -206 240 -206C166 -206 108 -165 108 -110C108 -82 128 -54 154 -32C172 -17 195 -11 241 -11Z" id="g121-101"></path></g><g transform="matrix(.0091,0,0,-0.0091,16.063,3.818)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path></g><g transform="matrix(.013,0,0,-0.013,21.01,0)"><path d="M290 -163V-135C183 -126 181 -122 181 -44V583C181 662 184 666 290 675V703H120V-163H290Z" id="g113-92"></path></g><g transform="matrix(.013,0,0,-0.013,25.494,0)"><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" id="g113-50"></path></g><g transform="matrix(.013,0,0,-0.013,31.734,0)"><path d="M368 703H309L44 -163H104L368 703Z" id="g113-48"></path></g><g transform="matrix(.013,0,0,-0.013,37.096,0)"><path d="M480 416C480 431 465 448 438 448C388 448 312 383 252 330C217 299 188 273 155 237H153L257 680C262 700 263 712 253 712C240 712 183 684 97 674L92 648L126 647C166 646 172 645 163 606L23 -6L29 -12C51 -5 77 2 107 8C115 62 130 128 142 180C153 193 179 220 204 241C231 170 259 106 288 54C317 0 336 -12 358 -12C381 -12 423 2 477 80L460 100C434 74 408 54 398 54C385 54 374 65 351 107C326 154 282 241 263 299C296 332 351 377 403 377C424 377 436 372 445 368C449 366 456 368 462 375C472 386 480 402 480 416Z" id="g113-108"></path></g><g transform="matrix(.013,0,0,-0.013,43.635,0)"><path d="M226 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H226Z" id="g113-94"></path></g></svg> plot for the same cluster.</div>

Advances in High Energy Physics

fig3

Figure 3

Figure 3: Azimuthal Anisotropy in High-Energy Nuclear Collision: An Approach Based on Complex Network Analysis 