{"id":173358,"date":"2023-11-13T03:37:32","date_gmt":"2023-11-13T02:37:32","guid":{"rendered":"https:\/\/datascientest.com\/en\/?p=173358"},"modified":"2023-11-13T03:40:13","modified_gmt":"2023-11-13T02:40:13","slug":"networkx-graph-theory-basic-functions-and-use","status":"publish","type":"post","link":"https:\/\/datascientest.com\/en\/networkx-graph-theory-basic-functions-and-use","title":{"rendered":"NetworkX: Graph theory, basic functions and use"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"173358\" class=\"elementor elementor-173358\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-dd3ade6 e-flex e-con-boxed e-con\" data-id=\"dd3ade6\" 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-4d760cf elementor-widget elementor-widget-heading\" data-id=\"4d760cf\" 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 is a very useful python library for modelling your data in the form of graphs. It also contains some classic graph theory algorithms (Dijkstra, PageRank, SImRank...) which we will present in this 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-c2d1eae e-flex e-con-boxed e-con\" data-id=\"c2d1eae\" 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-45298472 elementor-widget elementor-widget-heading\" data-id=\"45298472\" 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\">What is a graph? Introduction to Graph Theory<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-29f403c9 elementor-widget elementor-widget-text-editor\" data-id=\"29f403c9\" 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>A graph is a set of nodes (representing individuals, cities, products, text, images, etc.), and edges linking a subset of these nodes. The degree of a node in the graph is its number of neighbours (the vertices linked to it by edges).<\/p><p>Edges can be one-sided or symmetrical, so a graph can be directed or undirected.<\/p><p>The undirected graph represents the relationships of kinship (green) and love (pink) between the main characters of the Round Table:<\/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-6691869c elementor-widget elementor-widget-image\" data-id=\"6691869c\" 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<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"1846\" height=\"546\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/11\/image9.png\" class=\"attachment-full size-full wp-image-173375\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/11\/image9.png 1846w, https:\/\/datascientest.com\/en\/files\/2023\/11\/image9-300x89.png 300w, https:\/\/datascientest.com\/en\/files\/2023\/11\/image9-1024x303.png 1024w, https:\/\/datascientest.com\/en\/files\/2023\/11\/image9-768x227.png 768w, https:\/\/datascientest.com\/en\/files\/2023\/11\/image9-1536x454.png 1536w\" sizes=\"(max-width: 1846px) 100vw, 1846px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/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-e074109 elementor-widget elementor-widget-text-editor\" data-id=\"e074109\" 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>The following directed graph represents a list of tasks to be carried out to build a house:<\/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-883175f e-flex e-con-boxed e-con\" data-id=\"883175f\" 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-1fcdcf04 e-con-full e-flex e-con\" data-id=\"1fcdcf04\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2b35d76e elementor-widget elementor-widget-image\" data-id=\"2b35d76e\" 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=\"425\" height=\"634\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/11\/image12.png\" class=\"attachment-full size-full wp-image-173376\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/11\/image12.png 425w, https:\/\/datascientest.com\/en\/files\/2023\/11\/image12-201x300.png 201w\" sizes=\"(max-width: 425px) 100vw, 425px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/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>\n\t\t<div class=\"elementor-element elementor-element-cee785b e-con-full e-flex e-con\" data-id=\"cee785b\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-3aee78e8 elementor-widget elementor-widget-image\" data-id=\"3aee78e8\" 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=\"390\" height=\"252\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/11\/image7.png\" class=\"attachment-full size-full wp-image-173377\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/11\/image7.png 390w, https:\/\/datascientest.com\/en\/files\/2023\/11\/image7-300x194.png 300w\" sizes=\"(max-width: 390px) 100vw, 390px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/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>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-8c425ee e-flex e-con-boxed e-con\" data-id=\"8c425ee\" 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-78a26e7 elementor-widget elementor-widget-text-editor\" data-id=\"78a26e7\" 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>We can choose to weight the edges of a graph with weights modelling the cost or proportion of use of that path. For example, in the graph above, the cost of the edges would be the number of days needed to complete the task.<\/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-5a90b8c elementor-widget elementor-widget-heading\" data-id=\"5a90b8c\" 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-18c2ba3 elementor-widget elementor-widget-text-editor\" data-id=\"18c2ba3\" 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>Graph theory covers a vast range of applications: modelling networks (infrastructure, social, etc.), stock management, timetabling and their associated problems:<\/p><ul><li>How to establish the shortest\/optimal itinerary: the problem of the travelling salesman.<\/li><li>How to place infrastructure (electricity, fibre, etc.) in the best possible way? the problem of minimum coverage.<\/li><li>How do you allocate rentals to customers or courses to learners without overlapping? the colouring problem.<\/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-ffde3f2 e-flex e-con-boxed e-con\" data-id=\"ffde3f2\" 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-4709dab elementor-widget elementor-widget-heading\" data-id=\"4709dab\" 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\">Basic functions and main uses of NetworkX<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8e13f3f elementor-widget elementor-widget-heading\" data-id=\"8e13f3f\" 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\">Construct our first graph:<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e2e487a elementor-widget elementor-widget-text-editor\" data-id=\"e2e487a\" 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>The following code will build a graph, starting by adding its edges (g.addnode) and its nodes (g.add edge) (you can add several at once with the functions: g.add nodes from and g.add edges from), then display the graph created:<\/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-5419b03 elementor-widget elementor-widget-shortcode\" data-id=\"5419b03\" 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-60a28f4 elementor-widget elementor-widget-text-editor\" data-id=\"60a28f4\" 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>We can also quickly synthesise graph properties using NetworkX methods:<\/p><p>number of nodes with number_of_nodes, number of edges with number_of_edges<br \/>diameter = maximum distance between two nodes: diameter<\/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-b29792f elementor-widget elementor-widget-heading\" data-id=\"b29792f\" 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\">The Seven Bridges of Koenigsberg, what is this historical problem?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ed14f98 elementor-widget elementor-widget-text-editor\" data-id=\"ed14f98\" 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>One of the first problems in graph theory was the Koenigsberg bridge problem. It was presented to the mathematician Euler in 1736 in the following form:<\/p><p>&#8220;Can we cover all 7 bridges in the city by crossing each bridge only once? Euler noticed that the order of the journey had no influence and modelled the problem in the form of a graph: the various districts being its nodes, linked together by the bridges, which are therefore the edges of the graph.<\/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-b99e5f0 elementor-widget elementor-widget-image\" data-id=\"b99e5f0\" 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\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/12\/Fichier-84-8.png\" title=\"\" alt=\"networkx\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/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-8bc27cc elementor-widget elementor-widget-image\" data-id=\"8bc27cc\" 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\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image1-3.png\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Graph modelling the problem, edges are bridges, nodes are neighbourhoods<\/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-58e8eb4 elementor-widget elementor-widget-accordion\" data-id=\"58e8eb4\" 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-9321\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-9321\" 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\">So what do you think the solution is?<\/a>\n\t\t\t\t\t<\/h4>\n\t\t\t\t\t<div id=\"elementor-tab-content-9321\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-9321\"><p>If you arrive in a district via a bridge, you also have to leave it via (another) bridge. The number of arrivals in a district is therefore equal to the number of departures from that district. It follows that each neighbourhood must be linked to the others by an even number of bridges.<\/p><p>The solution to the problem therefore depends on the degree (number of adjoining neighbours\/bridges) of the nodes: if they are all even, then a path exists that crosses all the bridges once, called an Eulerian path.<\/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-36e6358 elementor-widget elementor-widget-shortcode\" data-id=\"36e6358\" 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-9631ee8 elementor-widget elementor-widget-heading\" data-id=\"9631ee8\" 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\">How do you find the shortest route with the Traveller's Problem?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-241a051 elementor-widget elementor-widget-text-editor\" data-id=\"241a051\" 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>Another classic graph-theoretic problem is that of the travelling salesman: the nodes of the graph are a set of towns or customers to be delivered to, while the edges are the road infrastructures, with a weight modelling the associated distance. The aim is to serve all the towns using the shortest route.<\/p><p>If the weights of the graph are positive (or at least if there is no cycle with a negative weight) a solution to this problem is given by <a href=\"https:\/\/datascientest.com\/en\/boosting-business-with-3-essential-machine-learning-algorithms\">Dijkstra&#8217;s algorithm, available via the function nx.shortest_path().<\/a><\/p><p>A smarter trainer than the others is trying to finish the adventure by taking the shortest possible route. The following script will enable him to reach the league in record time:<\/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-d072954 elementor-widget elementor-widget-shortcode\" data-id=\"d072954\" 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-5826bde e-flex e-con-boxed e-con\" data-id=\"5826bde\" 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-25f50a3 elementor-widget elementor-widget-heading\" data-id=\"25f50a3\" 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\">Minimum network coverage<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e5f96c3 elementor-widget elementor-widget-text-editor\" data-id=\"e5f96c3\" 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>The minimum spanning tree problem arises when a company wants to build a network (oil, fibre) connecting a <strong>set of households in the best possible way.<\/strong><\/p><p>In the graph associated with this problem, the nodes are the customers to be connected, the edges are the set of possible infrastructure locations and the weights are their construction costs.<\/p><p>The aim is to determine the subset of edges connecting all the nodes that minimises the total cost, known as the <strong>minimum spanning tree.<\/strong><\/p><p><strong>NetworkX<\/strong> has a function that solves this problem: the Kruskal algorithm implemented in the nx.tree.minimum_spanning_tree method.<\/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-618fb04 elementor-widget elementor-widget-shortcode\" data-id=\"618fb04\" 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-1e3f3bd elementor-widget elementor-widget-text-editor\" data-id=\"1e3f3bd\" 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>An industrialist wants to build a railway network in the fictitious province of Costaguana. He wants to connect all the towns but has a limited budget:<\/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-d4241ee elementor-widget elementor-widget-image\" data-id=\"d4241ee\" 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\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image6-1.png\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/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-9e9dd74 elementor-widget elementor-widget-text-editor\" data-id=\"9e9dd74\" 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>His problem will therefore be solved by displaying the minimal spanning tree associated with the graph (in green in the following images): the cost and number of edges saved can also be calculated:<\/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-55093a6 elementor-widget elementor-widget-image\" data-id=\"55093a6\" 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\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image11-1.png\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/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-5ecc6cb elementor-widget elementor-widget-image\" data-id=\"5ecc6cb\" 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\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/image2-1.png\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/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\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-f36d926 e-flex e-con-boxed e-con\" data-id=\"f36d926\" 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-3224a10 elementor-widget elementor-widget-heading\" data-id=\"3224a10\" 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-a65316a elementor-widget elementor-widget-text-editor\" data-id=\"a65316a\" 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>Page rank is an <a href=\"https:\/\/datascientest.com\/en\/google-deepmind-creates-ai-that-revolutionizes-sorting-algorithms\">algorithm used by Google<\/a> to calculate the popularity of web pages: those with the highest score are displayed first.<\/p><p>To measure this score, the web is represented by a graph in which the nodes are the websites and the edges are the hypertext links between the pages.<\/p><p>The principle is as follows: the initial scores of the graphs are uniform, we then go through the graph at random, jumping from one site to another at random (so we don&#8217;t take into account previously visited sites), and each time we go through a website we update its score.<\/p><p>At the end of the algorithm, the scores of the sites will be proportional to the probabilities of passage: the sites most visited by the random surfer\/walker will have a high score.<\/p><p>One of the main problems with PageRank is its very high calculation cost. A related algorithm, SimRank, which calculates the similarity between web pages, is also implemented by 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-8f15251 e-flex e-con-boxed e-con\" data-id=\"8f15251\" 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-d276f27 elementor-widget elementor-widget-heading\" data-id=\"d276f27\" 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-014d42b elementor-widget elementor-widget-text-editor\" data-id=\"014d42b\" 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 covers a range of effective methods for a vast array of applications. Find out more about its applications in Data Science with our Machine Learning and Graph Theory with NetworkX module in our Data Scientist course.<\/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-ee1c156 elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"ee1c156\" 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\/en\/data-courses\">\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\">Discover our Data Scientist Course<\/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\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>NetworkX is a very useful python library for modelling your data in the form of graphs. It also contains some classic graph theory algorithms (Dijkstra, PageRank, SImRank&#8230;) which we will present in this article. What is a graph? Introduction to Graph Theory A graph is a set of nodes (representing individuals, cities, products, text, images, [&hellip;]<\/p>\n","protected":false},"author":67,"featured_media":173365,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2425],"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: Graph theory, basic functions and use<\/title>\n<meta name=\"description\" content=\"Dive into the world of network analysis with NetworkX. 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