A Simple Visualization Method for Three-Dimensional (3D) Network

<div>Two possible forces at nodes <svg height="13.8999pt" id="M47" style="vertical-align:-3.94351pt" version="1.1" viewbox="-0.0498162 -9.95639 14.3172 13.8999" width="14.3172pt" 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="M700 0V35C631 42 609 53 567 118C509 208 460 288 401 381C449 447 492 506 526 546C567 595 594 607 658 615V650H417V615C481 603 484 593 465 557C441 512 406 457 375 417C333 483 302 536 285 568C273 591 271 603 326 615V650H25V615C93 608 120 591 148 544C201 461 242 391 290 312C233 226 163 135 127 90C98 57 63 41 8 35V0H259V35C192 46 183 54 207 97C228 137 269 202 316 273C390 149 413 111 423 93C440 61 445 47 379 35V0H700Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.043,-5.741)"><path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.043,3.784)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z"></path></g></svg> and <span class="nowrap"><svg height="16.1378pt" id="M48" style="vertical-align:-6.18141pt" version="1.1" viewbox="-0.0498162 -9.95639 14.3172 16.1378" width="14.3172pt" 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="M700 0V35C631 42 609 53 567 118C509 208 460 288 401 381C449 447 492 506 526 546C567 595 594 607 658 615V650H417V615C481 603 484 593 465 557C441 512 406 457 375 417C333 483 302 536 285 568C273 591 271 603 326 615V650H25V615C93 608 120 591 148 544C201 461 242 391 290 312C233 226 163 135 127 90C98 57 63 41 8 35V0H259V35C192 46 183 54 207 97C228 137 269 202 316 273C390 149 413 111 423 93C440 61 445 47 379 35V0H700Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.043,-5.741)"><path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.043,3.784)"><path d="M400 606C400 634 383 656 353 656C316 656 294 620 294 593C294 564 317 545 343 545C375 545 400 573 400 606ZM366 351C379 413 381 451 356 451C323 451 251 408 183 341L199 313C223 335 267 365 277 365C285 365 284 354 277 312C245 132 222 27 193 -100C182 -148 160 -188 131 -188C113 -188 90 -178 75 -170C64 -164 55 -168 48 -175C38 -185 24 -203 24 -222S48 -257 71 -257C89 -257 131 -241 186 -192C243 -141 286 -46 310 74L366 351Z"></path></g></svg>:</span> (a) repulsive force when <svg height="16.1378pt" id="M49" style="vertical-align:-6.18141pt" version="1.1" viewbox="-0.0498162 -9.95639 77.2856 16.1378" width="77.2856pt" 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="M162 -163V703H101V-163H162Z"></path></g><g transform="matrix(.013,0,0,-0.013,3.419,0)"><path d="M700 0V35C631 42 609 53 567 118C509 208 460 288 401 381C449 447 492 506 526 546C567 595 594 607 658 615V650H417V615C481 603 484 593 465 557C441 512 406 457 375 417C333 483 302 536 285 568C273 591 271 603 326 615V650H25V615C93 608 120 591 148 544C201 461 242 391 290 312C233 226 163 135 127 90C98 57 63 41 8 35V0H259V35C192 46 183 54 207 97C228 137 269 202 316 273C390 149 413 111 423 93C440 61 445 47 379 35V0H700Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.462,-5.741)"><path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.462,3.784)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z"></path></g><g transform="matrix(.013,0,0,-0.013,20.542,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,31.078,0)"><path d="M700 0V35C631 42 609 53 567 118C509 208 460 288 401 381C449 447 492 506 526 546C567 595 594 607 658 615V650H417V615C481 603 484 593 465 557C441 512 406 457 375 417C333 483 302 536 285 568C273 591 271 603 326 615V650H25V615C93 608 120 591 148 544C201 461 242 391 290 312C233 226 163 135 127 90C98 57 63 41 8 35V0H259V35C192 46 183 54 207 97C228 137 269 202 316 273C390 149 413 111 423 93C440 61 445 47 379 35V0H700Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,40.121,-5.741)"><path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 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23 111C23 26 57 -12 91 -12C120 -12 147 3 188 29C227 54 290 102 341 170H343L322 71C308 6 320 -12 341 -12C373 -12 442 27 501 96L485 120C455 91 422 67 408 67C401 67 401 76 404 91C440 294 479 473 530 686ZM387 375L355 241C326 187 200 53 142 53C126 53 109 73 109 130C109 217 154 337 218 381C240 396 265 404 297 404S372 390 387 375Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,70.76,3.132)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,72.641,3.132)"><path d="M400 606C400 634 383 656 353 656C316 656 294 620 294 593C294 564 317 545 343 545C375 545 400 573 400 606ZM366 351C379 413 381 451 356 451C323 451 251 408 183 341L199 313C223 335 267 365 277 365C285 365 284 354 277 312C245 132 222 27 193 -100C182 -148 160 -188 131 -188C113 -188 90 -178 75 -170C64 -164 55 -168 48 -175C38 -185 24 -203 24 -222S48 -257 71 -257C89 -257 131 -241 186 -192C243 -141 286 -46 310 74L366 351Z"></path></g></svg> and (b) attractive force <svg height="16.1378pt" id="M50" style="vertical-align:-6.18141pt" version="1.1" viewbox="-0.0498162 -9.95639 77.2856 16.1378" width="77.2856pt" 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="M162 -163V703H101V-163H162Z"></path></g><g transform="matrix(.013,0,0,-0.013,3.419,0)"><path d="M700 0V35C631 42 609 53 567 118C509 208 460 288 401 381C449 447 492 506 526 546C567 595 594 607 658 615V650H417V615C481 603 484 593 465 557C441 512 406 457 375 417C333 483 302 536 285 568C273 591 271 603 326 615V650H25V615C93 608 120 591 148 544C201 461 242 391 290 312C233 226 163 135 127 90C98 57 63 41 8 35V0H259V35C192 46 183 54 207 97C228 137 269 202 316 273C390 149 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Discrete Dynamics in Nature and Society

A Simple Visualization Method for Three-Dimensional (3D) Network

Figure 2