graphes.svg (57036B)
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rdf:resource="http://purl.org/dc/dcmitype/StillImage" /> 487 <dc:title></dc:title> 488 </cc:Work> 489 </rdf:RDF> 490 </metadata> 491 <g 492 inkscape:label="Calque 1" 493 inkscape:groupmode="layer" 494 id="layer1"> 495 <text 496 xml:space="preserve" 497 style="font-size:5.64444px;line-height:1.25;font-family:'Noto Sans';-inkscape-font-specification:'Noto Sans';letter-spacing:0px;word-spacing:0px;stroke-width:0.264583" 498 x="28.604469" 499 y="23.512203" 500 id="text12"><tspan 501 sodipodi:role="line" 502 id="tspan10" 503 x="28.604469" 504 y="23.512203" 505 style="stroke-width:0.264583" /></text> 506 <text 507 xml:space="preserve" 508 style="font-size:5.64444px;line-height:1.25;font-family:'Noto Sans';-inkscape-font-specification:'Noto Sans';letter-spacing:0px;word-spacing:0px;stroke-width:0.264583" 509 x="16.391392" 510 y="38.841145" 511 id="text16"><tspan 512 sodipodi:role="line" 513 x="16.391392" 514 y="38.841145" 515 style="font-size:4.23333px;stroke-width:0.264583" 516 id="tspan34"><tspan 517 style="font-weight:bold;font-size:4.23333px" 518 id="tspan32">Graphe :</tspan> ensemble de<tspan 519 style="font-style:italic;font-weight:normal;font-size:4.23333px" 520 id="tspan50"> <tspan 521 style="font-weight:bold;font-size:4.23333px" 522 id="tspan70">sommets</tspan></tspan> reliés par des <tspan 523 style="font-style:italic;font-weight:bold;font-size:4.23333px" 524 id="tspan60">arêtes</tspan>.</tspan><tspan 525 sodipodi:role="line" 526 x="16.391392" 527 y="45.896694" 528 style="font-size:4.23333px;stroke-width:0.264583" 529 id="tspan80" /><tspan 530 sodipodi:role="line" 531 x="16.391392" 532 y="52.952244" 533 style="font-size:4.23333px;stroke-width:0.264583" 534 id="tspan18"><tspan 535 style="font-weight:bold;font-size:4.23333px" 536 id="tspan24">Sommets :</tspan> les points du graphe, représentent les <tspan 537 style="font-style:italic;font-weight:bold;font-size:4.23333px" 538 id="tspan64">utilisateurs</tspan></tspan><tspan 539 sodipodi:role="line" 540 x="16.391392" 541 y="60.007793" 542 style="font-size:4.23333px;stroke-width:0.264583" 543 id="tspan46">dans un réseau social par exemple.</tspan><tspan 544 sodipodi:role="line" 545 x="16.391392" 546 y="67.063347" 547 style="font-size:4.23333px;stroke-width:0.264583" 548 id="tspan82" /><tspan 549 sodipodi:role="line" 550 x="16.391392" 551 y="74.118896" 552 style="font-size:4.23333px;stroke-width:0.264583" 553 id="tspan20"><tspan 554 style="font-weight:bold;font-size:4.23333px" 555 id="tspan48">Arêtes :</tspan> les <tspan 556 style="font-style:italic;font-weight:bold;font-size:4.23333px" 557 id="tspan66">liens</tspan> entre les sommets, représentent les <tspan 558 style="font-style:italic;font-weight:bold;font-size:4.23333px" 559 id="tspan78">relations</tspan></tspan><tspan 560 sodipodi:role="line" 561 x="16.391392" 562 y="81.174446" 563 style="font-size:4.23333px;stroke-width:0.264583" 564 id="tspan76">entre les utilisateurs d’un réseau social.</tspan><tspan 565 sodipodi:role="line" 566 x="16.391392" 567 y="88.229996" 568 style="font-size:4.23333px;stroke-width:0.264583" 569 id="tspan1008" /><tspan 570 sodipodi:role="line" 571 x="16.391392" 572 y="95.285545" 573 style="font-size:4.23333px;stroke-width:0.264583" 574 id="tspan1010">Il y a 2 types d'arêtes :</tspan><tspan 575 sodipodi:role="line" 576 x="16.391392" 577 y="102.34109" 578 style="font-size:4.23333px;stroke-width:0.264583" 579 id="tspan1012">- dans les <tspan 580 style="font-weight:bold" 581 id="tspan1020">graphes orientés</tspan> les arêtes ont un <tspan 582 style="font-weight:bold" 583 id="tspan1022">sens</tspan>,</tspan><tspan 584 sodipodi:role="line" 585 x="16.391392" 586 y="109.39664" 587 style="font-size:4.23333px;stroke-width:0.264583" 588 id="tspan1014"> ça correspond par exemple au fait d'être <tspan 589 style="font-weight:bold" 590 id="tspan1032">abonné</tspan> à</tspan><tspan 591 sodipodi:role="line" 592 x="16.391392" 593 y="116.45219" 594 style="font-size:4.23333px;stroke-width:0.264583" 595 id="tspan1018"> un compte sur un réseau social</tspan><tspan 596 sodipodi:role="line" 597 x="16.391392" 598 y="123.50774" 599 style="font-size:4.23333px;stroke-width:0.264583" 600 id="tspan1038" /><tspan 601 sodipodi:role="line" 602 x="16.391392" 603 y="130.56329" 604 style="font-size:4.23333px;stroke-width:0.264583" 605 id="tspan1026">- dans les <tspan 606 style="font-weight:bold" 607 id="tspan1034">graphes non orientés</tspan> les arêtes vont</tspan><tspan 608 sodipodi:role="line" 609 x="16.391392" 610 y="137.61885" 611 style="font-size:4.23333px;stroke-width:0.264583" 612 id="tspan1028"> forcement dans les 2 sens, comme quand 2 personnes</tspan><tspan 613 sodipodi:role="line" 614 x="16.391392" 615 y="144.67439" 616 style="font-size:4.23333px;stroke-width:0.264583" 617 id="tspan1030"> sont <tspan 618 style="font-weight:bold" 619 id="tspan1036">amies</tspan> sur un réseau social</tspan><tspan 620 sodipodi:role="line" 621 x="16.391392" 622 y="151.72995" 623 style="font-size:4.23333px;stroke-width:0.264583" 624 id="tspan1466" /><tspan 625 sodipodi:role="line" 626 x="16.391392" 627 y="158.78549" 628 style="font-size:4.23333px;stroke-width:0.264583" 629 id="tspan1468"><tspan 630 style="font-weight:bold" 631 id="tspan1470">Chemin</tspan> : suite de sommets chacun relié au suivant par une arête.</tspan><tspan 632 sodipodi:role="line" 633 x="16.391392" 634 y="165.84105" 635 style="font-size:4.23333px;stroke-width:0.264583" 636 id="tspan1650" /><tspan 637 sodipodi:role="line" 638 x="16.391392" 639 y="172.89659" 640 style="font-size:4.23333px;stroke-width:0.264583" 641 id="tspan1654"><tspan 642 style="font-weight:bold" 643 id="tspan1656">Distance</tspan> entre 2 sommets : nombre d'arêtes du plus court</tspan><tspan 644 sodipodi:role="line" 645 x="16.391392" 646 y="179.95215" 647 style="font-size:4.23333px;stroke-width:0.264583" 648 id="tspan1658">chemin entre ces 2 sommets.</tspan><tspan 649 sodipodi:role="line" 650 x="16.391392" 651 y="187.00771" 652 style="font-size:4.23333px;stroke-width:0.264583" 653 id="tspan1836" /><tspan 654 sodipodi:role="line" 655 x="16.391392" 656 y="194.06325" 657 style="font-size:4.23333px;stroke-width:0.264583" 658 id="tspan1838"><tspan 659 style="font-weight:bold" 660 id="tspan1840">Diamètre</tspan> d'un graphe : la distance entre les 2 sommets les plus éloignés du graphe</tspan><tspan 661 sodipodi:role="line" 662 x="16.391392" 663 y="201.1188" 664 style="font-size:4.23333px;stroke-width:0.264583" 665 id="tspan1846">(plus grande distance entre 2 sommets du graphe).</tspan><tspan 666 sodipodi:role="line" 667 x="16.391392" 668 y="208.17435" 669 style="font-size:4.23333px;stroke-width:0.264583" 670 id="tspan1848" /><tspan 671 sodipodi:role="line" 672 x="16.391392" 673 y="215.2299" 674 style="font-size:4.23333px;stroke-width:0.264583" 675 id="tspan1850"><tspan 676 style="font-weight:bold" 677 id="tspan1852">Centre</tspan> d'un graphe : le sommet qui a une distance minimale avec tous les autres</tspan><tspan 678 sodipodi:role="line" 679 x="16.391392" 680 y="222.28545" 681 style="font-size:4.23333px;stroke-width:0.264583" 682 id="tspan1854">sommets du graphe (il peut y avoir plusieurs centres).</tspan><tspan 683 sodipodi:role="line" 684 x="16.391392" 685 y="229.341" 686 style="font-size:4.23333px;stroke-width:0.264583" 687 id="tspan1856" /><tspan 688 sodipodi:role="line" 689 x="16.391392" 690 y="236.39655" 691 style="font-size:4.23333px;stroke-width:0.264583" 692 id="tspan1858"><tspan 693 style="font-weight:bold" 694 id="tspan1860">Rayon</tspan> d'un graphe : distance entre le centre d'un graphe et le sommet le plus éloigné</tspan><tspan 695 sodipodi:role="line" 696 x="16.391392" 697 y="243.4521" 698 style="font-size:4.23333px;stroke-width:0.264583" 699 id="tspan1866">du centre.</tspan><tspan 700 sodipodi:role="line" 701 x="16.391392" 702 y="250.50764" 703 style="font-size:4.23333px;stroke-width:0.264583" 704 id="tspan1842" /><tspan 705 sodipodi:role="line" 706 x="16.391392" 707 y="257.5632" 708 style="font-size:4.23333px;stroke-width:0.264583" 709 id="tspan1844" /></text> 710 <g 711 id="g937" 712 transform="matrix(0.71618967,0,0,0.71618967,140.67877,-18.948704)" 713 style="stroke-width:1.39628"> 714 <circle 715 style="fill:none;stroke:#000000;stroke-width:1.39628;stroke-linecap:round;stroke-linejoin:bevel;stroke-miterlimit:4;stroke-dasharray:none;paint-order:fill markers stroke;stop-color:#000000" 716 id="path84" 717 cx="31.969341" 718 cy="110.29982" 719 r="13.085403" /> 720 <text 721 xml:space="preserve" 722 style="font-size:5.64444px;line-height:1.25;font-family:'Noto Sans';-inkscape-font-specification:'Noto Sans';text-align:center;letter-spacing:0px;word-spacing:0px;text-anchor:middle;stroke-width:0.369431" 723 x="31.887493" 724 y="112.0909" 725 id="text911"><tspan 726 sodipodi:role="line" 727 id="tspan909" 728 x="31.887493" 729 y="112.0909" 730 style="text-align:center;text-anchor:middle;stroke-width:0.369431">Sommet</tspan><tspan 731 sodipodi:role="line" 732 x="31.887493" 733 y="119.14645" 734 style="text-align:center;text-anchor:middle;stroke-width:0.369431" 735 id="tspan913" /></text> 736 </g> 737 <g 738 id="g990" 739 transform="matrix(0.50087381,-0.34951056,0.33920656,0.48610744,94.738484,30.825175)" 740 style="stroke-width:1.66197"> 741 <g 742 id="g995"> 743 <path 744 style="fill:none;stroke:#000000;stroke-width:1.66197;stroke-linecap:round;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1" 745 d="M 79.471039,100.87701 103.17476,94.36612" 746 id="path931" 747 sodipodi:nodetypes="cc" /> 748 <text 749 xml:space="preserve" 750 style="font-size:5.64444px;line-height:1.25;font-family:'Noto Sans';-inkscape-font-specification:'Noto Sans';letter-spacing:0px;word-spacing:0px;stroke-width:0.43973" 751 x="50.56189" 752 y="116.81807" 753 id="text955" 754 transform="rotate(-15.559823)"><tspan 755 sodipodi:role="line" 756 id="tspan953" 757 x="50.56189" 758 y="116.81807" 759 style="font-size:7.0357px;stroke-width:0.43973">Arête</tspan></text> 760 </g> 761 <path 762 style="fill:none;stroke:#000000;stroke-width:1.66197;stroke-linecap:round;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1" 763 d="m 65.353577,122.93388 6.318941,24.42377" 764 id="path997" 765 sodipodi:nodetypes="cc" /> 766 <text 767 xml:space="preserve" 768 style="font-size:5.64444px;line-height:1.25;font-family:'Noto Sans';-inkscape-font-specification:'Noto Sans';letter-spacing:0px;word-spacing:0px;stroke-width:0.43973" 769 x="136.57503" 770 y="-35.378868" 771 id="text1001" 772 transform="matrix(0.26033619,0.9926144,-0.93495013,0.27639277,0,0)"><tspan 773 sodipodi:role="line" 774 id="tspan999" 775 x="136.57503" 776 y="-35.378868" 777 style="font-size:7.0357px;stroke-width:0.43973">Arête</tspan></text> 778 </g> 779 <text 780 xml:space="preserve" 781 style="font-size:5.64444px;line-height:1.25;font-family:'Noto Sans';-inkscape-font-specification:'Noto Sans';text-align:center;letter-spacing:0px;word-spacing:0px;text-anchor:middle;stroke-width:0.264583" 782 x="104.85183" 783 y="17.440674" 784 id="text963"><tspan 785 sodipodi:role="line" 786 id="tspan961" 787 x="104.85183" 788 y="17.440674" 789 style="font-size:8.46667px;text-align:center;text-anchor:middle;stroke-width:0.264583;font-style:italic">Comment représenter les réseaux sociaux ?</tspan><tspan 790 sodipodi:role="line" 791 x="104.85183" 792 y="28.024012" 793 style="font-size:8.46667px;text-align:center;text-anchor:middle;stroke-width:0.264583;font-weight:bold" 794 id="tspan965">Les graphes</tspan></text> 795 <g 796 id="g975" 797 transform="matrix(0.71618967,0,0,0.71618967,161.84545,-45.407039)" 798 style="stroke-width:1.39628"> 799 <circle 800 style="fill:none;stroke:#000000;stroke-width:1.39628;stroke-linecap:round;stroke-linejoin:bevel;stroke-miterlimit:4;stroke-dasharray:none;paint-order:fill markers stroke;stop-color:#000000" 801 id="circle967" 802 cx="31.969341" 803 cy="110.29982" 804 r="13.085403" /> 805 <text 806 xml:space="preserve" 807 style="font-size:5.64444px;line-height:1.25;font-family:'Noto Sans';-inkscape-font-specification:'Noto Sans';text-align:center;letter-spacing:0px;word-spacing:0px;text-anchor:middle;stroke-width:0.369431" 808 x="31.887493" 809 y="112.0909" 810 id="text973"><tspan 811 sodipodi:role="line" 812 id="tspan969" 813 x="31.887493" 814 y="112.0909" 815 style="text-align:center;text-anchor:middle;stroke-width:0.369431">Sommet</tspan><tspan 816 sodipodi:role="line" 817 x="31.887493" 818 y="119.14645" 819 style="text-align:center;text-anchor:middle;stroke-width:0.369431" 820 id="tspan971" /></text> 821 </g> 822 <g 823 id="g985" 824 transform="matrix(0.71618967,0,0,0.71618967,165.54964,4.3346296)" 825 style="stroke-width:1.39628"> 826 <circle 827 style="fill:none;stroke:#000000;stroke-width:1.39628;stroke-linecap:round;stroke-linejoin:bevel;stroke-miterlimit:4;stroke-dasharray:none;paint-order:fill markers stroke;stop-color:#000000" 828 id="circle977" 829 cx="31.969341" 830 cy="110.29982" 831 r="13.085403" /> 832 <text 833 xml:space="preserve" 834 style="font-size:5.64444px;line-height:1.25;font-family:'Noto Sans';-inkscape-font-specification:'Noto Sans';text-align:center;letter-spacing:0px;word-spacing:0px;text-anchor:middle;stroke-width:0.369431" 835 x="31.887493" 836 y="112.0909" 837 id="text983"><tspan 838 sodipodi:role="line" 839 id="tspan979" 840 x="31.887493" 841 y="112.0909" 842 style="text-align:center;text-anchor:middle;stroke-width:0.369431">Sommet</tspan><tspan 843 sodipodi:role="line" 844 x="31.887493" 845 y="119.14645" 846 style="text-align:center;text-anchor:middle;stroke-width:0.369431" 847 id="tspan981" /></text> 848 </g> 849 <circle 850 style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:round;stroke-linejoin:bevel;stroke-miterlimit:4;stroke-dasharray:none;paint-order:fill markers stroke;stop-color:#000000" 851 id="path1040" 852 cx="144.17447" 853 cy="104.02051" 854 r="5.464747" /> 855 <circle 856 style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:round;stroke-linejoin:bevel;stroke-miterlimit:4;stroke-dasharray:none;paint-order:fill markers stroke;stop-color:#000000" 857 id="circle1044" 858 cx="170.63283" 859 cy="104.02051" 860 r="5.464747" /> 861 <path 862 style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2Send)" 863 d="m 149.7147,104.22042 h 14.13531" 864 id="path1046" /> 865 <circle 866 style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:round;stroke-linejoin:bevel;stroke-miterlimit:4;stroke-dasharray:none;paint-order:fill markers stroke;stop-color:#000000" 867 id="circle1400" 868 cx="144.17447" 869 cy="135.77051" 870 r="5.464747" /> 871 <circle 872 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