{"id":183372,"date":"2022-12-07T13:54:33","date_gmt":"2022-12-07T13:54:33","guid":{"rendered":"https:\/\/datascientest.com\/?p=183372"},"modified":"2023-11-09T13:55:26","modified_gmt":"2023-11-09T13:55:26","slug":"networkx-tout-savoir","status":"publish","type":"post","link":"https:\/\/datascientest.com\/networkx-tout-savoir","title":{"rendered":"NetworkX : Th\u00e9orie des graphes, fonctions de base et utilisation"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"183372\" class=\"elementor elementor-183372\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-08f2b29 e-flex e-con-boxed e-con\" data-id=\"08f2b29\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-b74c9bb elementor-widget elementor-widget-heading\" data-id=\"b74c9bb\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">NetworkX est une librairie python tr\u00e8s utile pour mod\u00e9liser vos donn\u00e9es sous forme de graphes. Elle contient \u00e9galement des algorithmes classiques de th\u00e9orie des graphes (Dijkstra, PageRank, SImRank...) que nous allons pr\u00e9senter dans cet article.<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-e7839e6 e-flex e-con-boxed e-con\" data-id=\"e7839e6\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-15c2958 elementor-widget elementor-widget-heading\" data-id=\"15c2958\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Qu\u2019est ce qu\u2019un graphe ? Introduction \u00e0 la Th\u00e9orie des Graphes<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d4c33fa elementor-widget elementor-widget-text-editor\" data-id=\"d4c33fa\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p>Un graphe est un <strong>ensemble de n\u0153uds<\/strong> (repr\u00e9sentant individu, villes, produits, texte, image, etc.), et d\u2019ar\u00eates reliant un sous-ensemble de ces n\u0153uds. Le degr\u00e9 d\u2019un n\u0153ud du graphe est son nombre de voisins (les sommets reli\u00e9s \u00e0 lui par des ar\u00eates).<\/p><p>Les ar\u00eates peuvent \u00eatre <strong>unilat\u00e9rales ou sym\u00e9triques<\/strong>, un graphe peut donc \u00eatre orient\u00e9 ou non.<\/p><p>Le graphe non orient\u00e9 repr\u00e9sente les relations de parent\u00e9s (en vert) et d\u2019amour (en rose ) des personnages principaux de la table ronde :<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4c212b2 elementor-widget elementor-widget-image\" data-id=\"4c212b2\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"1846\" height=\"546\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image9.png\" class=\"attachment-full size-full wp-image-183375\" alt=\"\" loading=\"lazy\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image9.png 1846w, https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image9-300x89.png 300w, https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image9-1024x303.png 1024w, https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image9-768x227.png 768w, https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image9-1536x454.png 1536w\" sizes=\"(max-width: 1846px) 100vw, 1846px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9ed09ea elementor-widget elementor-widget-text-editor\" data-id=\"9ed09ea\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\tLe graphe orient\u00e9 suivant repr\u00e9sente une liste de t\u00e2ches \u00e0 effectuer pour construire une maison :\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-5f762a2 e-flex e-con-boxed e-con\" data-id=\"5f762a2\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-3f3cb1f e-con-full e-flex e-con\" data-id=\"3f3cb1f\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-bbd784b elementor-widget elementor-widget-image\" data-id=\"bbd784b\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"425\" height=\"634\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image12.png\" class=\"attachment-full size-full wp-image-183376\" alt=\"\" loading=\"lazy\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image12.png 425w, https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image12-201x300.png 201w\" sizes=\"(max-width: 425px) 100vw, 425px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-2366328 e-con-full e-flex e-con\" data-id=\"2366328\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-d74484f elementor-widget elementor-widget-image\" data-id=\"d74484f\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"390\" height=\"252\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image7.png\" class=\"attachment-full size-full wp-image-183377\" alt=\"\" loading=\"lazy\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image7.png 390w, https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image7-300x194.png 300w\" sizes=\"(max-width: 390px) 100vw, 390px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-c34b22c e-flex e-con-boxed e-con\" data-id=\"c34b22c\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-0ba368d elementor-widget elementor-widget-text-editor\" data-id=\"0ba368d\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>On peut choisir de <strong>pond\u00e9rer les ar\u00eates d\u2019un graphe<\/strong> avec des poids mod\u00e9lisant le co\u00fbt ou la proportion d\u2019usage de ce chemin. Par exemple, sur le graphe pr\u00e9c\u00e9dent, le co\u00fbt des ar\u00eates serait le nombre de jours n\u00e9cessaires pour r\u00e9aliser la t\u00e2che.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a3824c9 elementor-widget elementor-widget-heading\" data-id=\"a3824c9\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Applications :<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6d3d04d elementor-widget elementor-widget-text-editor\" data-id=\"6d3d04d\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>La th\u00e9orie des graphes recouvre un ensemble vaste d\u2019applications : mod\u00e9lisation de r\u00e9seaux (infrastructures, sociaux\u2026), de gestion de stocks, d\u2019emploi du temps et leurs probl\u00e9matiques associ\u00e9es :<\/p><ul><li>Comment \u00e9tablir l\u2019itin\u00e9raire le plus court\/optimal ? probl\u00e8me du voyageur de commerce.<\/li><li>Comment placer des infrastructures (\u00e9lectriques, fibre&#8230;) de fa\u00e7on optimale ? probl\u00e8me de couverture minimale.<\/li><li>Comment allouer des locations \u00e0 des clients ou des cours \u00e0 des apprenants sans chevauchement ? probl\u00e8me de coloration.<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-c591a16 e-flex e-con-boxed e-con\" data-id=\"c591a16\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-c131417 elementor-widget elementor-widget-heading\" data-id=\"c131417\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Fonctions de base et principales utilisations de NetworkX<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6dd150b elementor-widget elementor-widget-heading\" data-id=\"6dd150b\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Construire notre premier graphe :<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-caf29c6 elementor-widget elementor-widget-text-editor\" data-id=\"caf29c6\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Le code suivant va construire un graphe, on commence par lui ajouter ses ar\u00eates (<strong><em>g.addnode<\/em><\/strong>) et ses n\u0153uds (<strong><em>g.add edge<\/em><\/strong>) (on peut en ajouter plusieurs \u00e0 la fois avec les fonctions: <strong><em>g.add nodes from et g.add edges from<\/em><\/strong>), on affiche ensuite le graphe cr\u00e9\u00e9 :<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b388657 elementor-widget elementor-widget-shortcode\" data-id=\"b388657\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><script src=\"https:\/\/gist.github.com\/robinTdatascientest\/c4409afed360fd62acb00011699ef9ff.js\"><\/script><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-56958a0 elementor-widget elementor-widget-text-editor\" data-id=\"56958a0\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>On peut aussi synth\u00e9tiser rapidement des propri\u00e9t\u00e9s du graphe via les m\u00e9thodes de NetworkX:<\/p><ul><li>nombre de noeuds avec <em>number_of_nodes<\/em>, nombre d\u2019ar\u00eates avec <em>number_of_edges<\/em><\/li><li>diam\u00e8tre = distance maximale entre deux noeuds : <em>diameter<\/em><\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-14ddf5a elementor-widget elementor-widget-heading\" data-id=\"14ddf5a\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Les Sept Ponts de Koenigsberg, quel est ce probl\u00e8me historique ?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-aebba7f elementor-widget elementor-widget-text-editor\" data-id=\"aebba7f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Un des premiers probl\u00e8mes de la th\u00e9orie des graphes est celui des <strong>ponts de Koenigsberg<\/strong>. Il fut pr\u00e9sent\u00e9 en 1736 au math\u00e9maticien Euler sous la forme suivante :<\/p><p>\u00ab\u00a0Peut-on parcourir les 7 ponts de la ville en empruntant chaque pont une seule fois ?\u00a0\u00bb: Euler remarqua que l\u2019ordre du parcours n\u2019avait aucune influence et mod\u00e9lisa le probl\u00e8me sous forme d\u2019un graphe : les diff\u00e9rents quartiers \u00e9tant ses n\u0153uds, reli\u00e9s entre eux par les ponts, qui sont donc les ar\u00eates du graphe.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6e6efc8 elementor-widget elementor-widget-image\" data-id=\"6e6efc8\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"604\" height=\"198\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/12\/Fichier-84-8.png\" class=\"attachment-full size-full wp-image-185151\" alt=\"networkx\" loading=\"lazy\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/12\/Fichier-84-8.png 604w, https:\/\/datascientest.com\/wp-content\/uploads\/2022\/12\/Fichier-84-8-300x98.png 300w\" sizes=\"(max-width: 604px) 100vw, 604px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-93baaf0 elementor-widget elementor-widget-image\" data-id=\"93baaf0\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"516\" height=\"633\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image1-3.png\" class=\"attachment-full size-full wp-image-183382\" alt=\"\" loading=\"lazy\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image1-3.png 516w, https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image1-3-245x300.png 245w\" sizes=\"(max-width: 516px) 100vw, 516px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Graphe mod\u00e9lisant le probl\u00e8me, les ar\u00eates sont les ponts, les noeuds les quartiers<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d49b649 elementor-widget elementor-widget-accordion\" data-id=\"d49b649\" data-element_type=\"widget\" data-widget_type=\"accordion.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>.elementor-accordion{text-align:left}.elementor-accordion .elementor-accordion-item{border:1px solid #d5d8dc}.elementor-accordion .elementor-accordion-item+.elementor-accordion-item{border-top:none}.elementor-accordion .elementor-tab-title{margin:0;padding:15px 20px;font-weight:700;line-height:1;cursor:pointer;outline:none}.elementor-accordion .elementor-tab-title .elementor-accordion-icon{display:inline-block;width:1.5em}.elementor-accordion .elementor-tab-title .elementor-accordion-icon svg{width:1em;height:1em}.elementor-accordion .elementor-tab-title .elementor-accordion-icon.elementor-accordion-icon-right{float:right;text-align:right}.elementor-accordion .elementor-tab-title .elementor-accordion-icon.elementor-accordion-icon-left{float:left;text-align:left}.elementor-accordion .elementor-tab-title .elementor-accordion-icon .elementor-accordion-icon-closed{display:block}.elementor-accordion .elementor-tab-title .elementor-accordion-icon .elementor-accordion-icon-opened,.elementor-accordion .elementor-tab-title.elementor-active .elementor-accordion-icon-closed{display:none}.elementor-accordion .elementor-tab-title.elementor-active .elementor-accordion-icon-opened{display:block}.elementor-accordion .elementor-tab-content{display:none;padding:15px 20px;border-top:1px solid #d5d8dc}@media (max-width:767px){.elementor-accordion .elementor-tab-title{padding:12px 15px}.elementor-accordion .elementor-tab-title .elementor-accordion-icon{width:1.2em}.elementor-accordion .elementor-tab-content{padding:7px 15px}}.e-con-inner>.elementor-widget-accordion,.e-con>.elementor-widget-accordion{width:var(--container-widget-width);--flex-grow:var(--container-widget-flex-grow)}<\/style>\t\t<div class=\"elementor-accordion\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<h4 id=\"elementor-tab-title-2221\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2221\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-caret-square-down\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M448 80v352c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V80c0-26.5 21.5-48 48-48h352c26.5 0 48 21.5 48 48zM92.5 220.5l123 123c4.7 4.7 12.3 4.7 17 0l123-123c7.6-7.6 2.2-20.5-8.5-20.5H101c-10.7 0-16.1 12.9-8.5 20.5z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-far-caret-square-up\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M322.9 304H125.1c-10.7 0-16.1-13-8.5-20.5l98.9-98.3c4.7-4.7 12.2-4.7 16.9 0l98.9 98.3c7.7 7.5 2.3 20.5-8.4 20.5zM448 80v352c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V80c0-26.5 21.5-48 48-48h352c26.5 0 48 21.5 48 48zm-48 346V86c0-3.3-2.7-6-6-6H54c-3.3 0-6 2.7-6 6v340c0 3.3 2.7 6 6 6h340c3.3 0 6-2.7 6-6z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Alors quelle est la solution selon vous ?<\/a>\n\t\t\t\t\t<\/h4>\n\t\t\t\t\t<div id=\"elementor-tab-content-2221\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2221\"><p>Si l\u2019on arrive via un pont dans un quartier, il faut aussi le quitter par un (autre) pont. Le nombre d&rsquo;arriv\u00e9es dans un quartier est donc \u00e9gale au nombre de d\u00e9parts depuis ce quartier. Il en r\u00e9sulte que chaque quartier doit \u00eatre reli\u00e9 aux autres via un nombre pairs de ponts.<\/p><p>La solution du probl\u00e8me d\u00e9pend donc du degr\u00e9 (nombre de voisins\/ponts attenants) des n\u0153uds : si ceux-ci sont tous pairs alors un chemin empruntant tous les ponts une seule fois, nomm\u00e9 chemin eul\u00e9rien, existe.<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a9b6099 elementor-widget elementor-widget-shortcode\" data-id=\"a9b6099\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><script src=\"https:\/\/gist.github.com\/robinTdatascientest\/a21299c602542966157ad6acc0cc3253.js\"><\/script><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8260d8d elementor-widget elementor-widget-heading\" data-id=\"8260d8d\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Comment trouver le chemin le plus court avec le Probl\u00e8me du Voyageur de Commerce ?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-815d75d elementor-widget elementor-widget-text-editor\" data-id=\"815d75d\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Un autre probl\u00e8me classique de th\u00e9orie des graphes est celui du voyageur de commerce : les n\u0153uds du graphe sont un ensemble de villes ou de clients \u00e0 livrer tandis que les ar\u00eates sont les infrastructures routi\u00e8res, munies d\u2019un poids mod\u00e9lisant la distance associ\u00e9e. On cherche \u00e0 desservir toutes les villes en empruntant le chemin le plus court.<\/p><p>Dans le cas o\u00f9 les poids du graphe sont positifs (ou du moins s\u2019il n\u2019y a pas de cycle avec un poids n\u00e9gatif) une solution \u00e0 ce probl\u00e8me est donn\u00e9e par l\u2019<a href=\"https:\/\/datascientest.com\/algorithme-de-dijkstra\">algorithme de Dijkstra<\/a>, disponible via la <strong>fonction <em>nx.shortest_path()<\/em><\/strong>.<\/p><p>Un dresseur plus malin que les autre cherche \u00e0 finir l\u2019aventure en empruntant le moins de chemin possible, le script suivant lui permettra de rallier la ligue en un temps record :<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-63c7c62 elementor-widget elementor-widget-shortcode\" data-id=\"63c7c62\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><script src=\"https:\/\/gist.github.com\/robinTdatascientest\/174fe8c4d48d07dc07f16c23c88baf51.js\"><\/script><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-4764f29 e-flex e-con-boxed e-con\" data-id=\"4764f29\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-af42762 elementor-widget elementor-widget-heading\" data-id=\"af42762\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Couverture Minimale d\u2019un r\u00e9seau<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-274ad27 elementor-widget elementor-widget-text-editor\" data-id=\"274ad27\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Le probl\u00e8me de l\u2019arbre couvrant minimal se pose lorsqu\u2019une entreprise cherche \u00e0 construire un r\u00e9seau (p\u00e9trole, fibre) reliant un ensemble de foyers de fa\u00e7on optimale.<\/p><p>Dans le graphe associ\u00e9 \u00e0 ce probl\u00e8me, les n\u0153uds sont les clients \u00e0 relier, les ar\u00eates l\u2019ensemble des emplacements d\u2019infrastructures possibles et les poids sont leurs co\u00fbts de construction.<\/p><p>On cherche \u00e0 d\u00e9terminer le sous ensemble d\u2019ar\u00eates reliant l\u2019ensemble des n\u0153uds qui minimise le co\u00fbt total, nomm\u00e9 arbre couvrant minimal.<\/p><p>NetworkXdispose d&rsquo;une fonction r\u00e9solvant ce probl\u00e8me : l\u2019algorithme de Kruskal impl\u00e9ment\u00e9 dans la <strong>m\u00e9thode<\/strong> <em><strong>nx.tree.minimum_spanning_tree<\/strong><\/em><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6a53810 elementor-widget elementor-widget-shortcode\" data-id=\"6a53810\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><script src=\"https:\/\/gist.github.com\/robinTdatascientest\/9c41fbe79a22b081ae60b6dc4ae65ff0.js\"><\/script><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1838439 elementor-widget elementor-widget-text-editor\" data-id=\"1838439\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Un industriel cherche \u00e0 construire un r\u00e9seau de chemins de fer dans le province fictive du Costaguana, il veut relier toute les villes mais dispose d\u2019un budget limit\u00e9, il mod\u00e9lise la situation via le graphe suivant :<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1fd53e8 elementor-widget elementor-widget-image\" data-id=\"1fd53e8\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"518\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image6-1.png\" class=\"attachment-large size-large wp-image-183410\" alt=\"\" loading=\"lazy\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image6-1.png 892w, https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image6-1-300x194.png 300w, https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image6-1-768x498.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ab27338 elementor-widget elementor-widget-text-editor\" data-id=\"ab27338\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\tSon probl\u00e8me sera donc r\u00e9solu en affichant l&rsquo;arbre couvrant minimal associ\u00e9 au graphe (en vert sur les images suivantes) : on peut \u00e9galement calculer le co\u00fbt et le nombre d\u2019ar\u00eates \u00e9conomis\u00e9s :\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3ba9cd0 elementor-widget elementor-widget-image\" data-id=\"3ba9cd0\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"457\" height=\"731\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image11-1.png\" class=\"attachment-full size-full wp-image-183411\" alt=\"\" loading=\"lazy\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image11-1.png 457w, https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image11-1-188x300.png 188w\" sizes=\"(max-width: 457px) 100vw, 457px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-72a6821 elementor-widget elementor-widget-image\" data-id=\"72a6821\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"1171\" height=\"578\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image2-1.png\" class=\"attachment-full size-full wp-image-183412\" alt=\"\" loading=\"lazy\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image2-1.png 1171w, https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image2-1-300x148.png 300w, https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image2-1-1024x505.png 1024w, https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image2-1-768x379.png 768w\" sizes=\"(max-width: 1171px) 100vw, 1171px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-f5ac103 e-flex e-con-boxed e-con\" data-id=\"f5ac103\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-b8944e0 elementor-widget elementor-widget-heading\" data-id=\"b8944e0\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Page Rank :<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-55ea7b4 elementor-widget elementor-widget-text-editor\" data-id=\"55ea7b4\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Le <a href=\"https:\/\/datascientest.com\/algorithme-de-page-rank\">page rank<\/a> est un algorithme utilis\u00e9 par Google pour calculer la popularit\u00e9 des pages web : celles avec le plus gros score sont affich\u00e9es en premier.<\/p><p>Pour mesurer ce score, on repr\u00e9sente le web par un graphe dont les n\u0153uds sont les sites web et les ar\u00eates sont les liens hypertextes\/entre les pages. Le principe est le suivant : les scores initiaux des graphes sont uniformes, on va ensuite parcourir le graphe au hasard en sautant d\u2019un site \u00e0 un autre de fa\u00e7on al\u00e9atoire (on ne prend donc pas en compte les sites visit\u00e9s pr\u00e9c\u00e9demment), et \u00e0 chaque passage par un site web on va actualiser son score.<\/p><p>\u00c0 la fin de l\u2019algorithme, les scores des sites seront proportionnels aux probabilit\u00e9s de passage : les sites les plus visit\u00e9s par le surfeur\/marcheur al\u00e9atoire auront un score important.<\/p><p>L\u2019un des principaux probl\u00e8mes du <strong>PageRank<\/strong> est son co\u00fbt de calcul tr\u00e8s \u00e9lev\u00e9. Un algorithme connexe, le <strong>SimRank<\/strong>, qui calcule la calcule la similarit\u00e9 entre les pages webs est \u00e9galement impl\u00e9ment\u00e9 par NetworkX<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-d0e9291 e-flex e-con-boxed e-con\" data-id=\"d0e9291\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-e298b42 elementor-widget elementor-widget-heading\" data-id=\"e298b42\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Conclusion<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-dce9002 elementor-widget elementor-widget-text-editor\" data-id=\"dce9002\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>NetworkX recouvre donc un ensemble de m\u00e9thodes efficaces r\u00e9pondant \u00e0 un vaste champ d\u2019applications. D\u00e9couvrez davantage de ses applications \u00e0 la Data Science avec notre module <strong><a href=\"https:\/\/datascientest.com\/3-algorithmes-de-machine-learning-utiles-pour-votre-business\">Machine Learning<\/a> et Th\u00e9orie des graphes avec NetworkX de notre cursus Data Scientist<\/strong>.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9d5f349 elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"9d5f349\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/formation-data-scientist\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">D\u00e9couvrir le cursus Data Scientist<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-dd12b34 e-flex e-con-boxed e-con\" data-id=\"dd12b34\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-7518b73 elementor-widget elementor-widget-html\" data-id=\"7518b73\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<script type=\"application\/ld+json\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@type\": \"FAQPage\",\r\n  \"mainEntity\": [{\r\n    \"@type\": \"Question\",\r\n    \"name\": \"Qu\u2019est ce qu\u2019un graphe ? Introduction \u00e0 la Th\u00e9orie des Graphes\",\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"Un graphe est un ensemble de n\u0153uds (repr\u00e9sentant individu, villes, produits, texte, image, etc.), et d\u2019ar\u00eates reliant un sous-ensemble de ces n\u0153uds. Le degr\u00e9 d\u2019un n\u0153ud du graphe est son nombre de voisins (les sommets reli\u00e9s \u00e0 lui par des ar\u00eates). Les ar\u00eates peuvent \u00eatre unilat\u00e9rales ou sym\u00e9triques, un graphe peut donc \u00eatre orient\u00e9 ou non.\"\r\n    }\r\n  },{\r\n    \"@type\": \"Question\",\r\n    \"name\": \"Comment trouver le chemin le plus court avec le Probl\u00e8me du Voyageur de Commerce ?\u200b\",\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"Un autre probl\u00e8me classique de th\u00e9orie des graphes est celui du voyageur de commerce : les n\u0153uds du graphe sont un ensemble de villes ou de clients \u00e0 livrer tandis que les ar\u00eates sont les infrastructures routi\u00e8res, munies d\u2019un poids mod\u00e9lisant la distance associ\u00e9e. On cherche \u00e0 desservir toutes les villes en empruntant le chemin le plus court.\"\r\n    }\r\n  },{\r\n    \"@type\": \"Question\",\r\n    \"name\": \"Les Sept Ponts de Koenigsberg, quel est ce probl\u00e8me historique ?\u200b\",\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"Un des premiers probl\u00e8mes de la th\u00e9orie des graphes est celui des ponts de Koenigsberg. 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Introduction \u00e0 la Th\u00e9orie des Graphes Un graphe est un ensemble de n\u0153uds (repr\u00e9sentant individu, [&hellip;]<\/p>\n","protected":false},"author":77,"featured_media":185155,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2497],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NetworkX : Th\u00e9orie des graphes, fonctions de base et utilisation<\/title>\n<meta name=\"description\" content=\"NetworkX est une librairie python tr\u00e8s utile pour mod\u00e9liser vos donn\u00e9es sous forme de graphes. 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