{"id":182307,"date":"2024-03-20T01:13:00","date_gmt":"2024-03-20T00:13:00","guid":{"rendered":"https:\/\/datascientest.com\/en\/?p=182307"},"modified":"2024-03-09T14:19:14","modified_gmt":"2024-03-09T13:19:14","slug":"kruskal-algorithm-definition-and-purpose","status":"publish","type":"post","link":"https:\/\/datascientest.com\/en\/kruskal-algorithm-definition-and-purpose","title":{"rendered":"Kruskal Algorithm: Definition and Purpose"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"182307\" class=\"elementor elementor-182307\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-73f1d49 e-flex e-con-boxed e-con\" data-id=\"73f1d49\" 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-51ba40a elementor-widget elementor-widget-heading\" data-id=\"51ba40a\" 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\">Kruskal's algorithm for optimizing connections within a network is one of the key concepts in Machine Learning. Find out how it works and why it's so useful in everyday life.<\/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-13f2451 e-flex e-con-boxed e-con\" data-id=\"13f2451\" 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-d9acf24 elementor-widget elementor-widget-heading\" data-id=\"d9acf24\" 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 the Kruskal algorithm?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-274df98 elementor-widget elementor-widget-text-editor\" data-id=\"274df98\" 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>Designed in 1956 by Joseph Kruskal, Kruskal&#8217;s algorithm is used to find a minimum weight spanning tree (MWST) (also known as a minimum spanning tree (MST) or minimum subtending tree (MST)) in a non-oriented, weighted connected graph.<\/p><p>Before going into detail, we need to define the terms below:<\/p><ul><li><strong>Tree:<\/strong> corresponds to a connected graph with no cycle (or acyclic).<\/li><li><strong>Connected graph:<\/strong> this means that there is a path to all the vertices of the graph from any other vertex.<\/li><li><strong>Acyclic graph:<\/strong> this means that the cycle is interrupted to access all vertices.<\/li><li><strong>Weighted graph:<\/strong> each edge has a weight.<\/li><li><strong>Undirected graph:<\/strong> each edge can be traversed in either direction.<\/li><li><strong>Spanning tree:<\/strong> refers to a set of edges in a weighted graph that contains all vertices (but not necessarily all edges). The weight of the spanning tree is the sum of the weights of its edges.<\/li><li><strong>Minimum weight spanning tree (MWST):<\/strong> this is a spanning tree whose weight is as small as possible. In other words, it is a subset of edges that connects all the nodes in the graph where the sum of the edge weights is as low as possible.<\/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-bd409e8 elementor-widget elementor-widget-text-editor\" data-id=\"bd409e8\" 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 aim of Kruskal&#8217;s algorithm is to find this minimum-weight spanning tree.<\/p><p>Good to know: in addition to Kruskal&#8217;s algorithm, you can also use Prim&#8217;s algorithm to find an ARPM.<\/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-a1db7ff e-flex e-con-boxed e-con\" data-id=\"a1db7ff\" 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-0a4b188 elementor-widget elementor-widget-heading\" data-id=\"0a4b188\" 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 does the Kruskal algorithm work?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cfc41e4 elementor-widget elementor-widget-heading\" data-id=\"cfc41e4\" 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-medium\">The steps of the Kruskal algorithm<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7577a96 elementor-widget elementor-widget-text-editor\" data-id=\"7577a96\" 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>To find the least-weight spanning tree, the <strong>Kruskal algorithm provides the following steps:<\/strong><\/p><ul><li>Sort the edges (a) of the graph (G) by increasing weight. In doing so, the lightest edges are examined first.<\/li><li>Start with an empty tree (T). That is, a tree containing no edges; its weight is 0. Its construction is progressive, following these steps.<\/li><li>Select edges by ascending weight. Start with the lightest edges. If the addition of an edge does not imply the creation of a cycle in the graph, add it to the tree.<\/li><li>Repeat the operation until all vertices (S) are connected. And this without creating a cycle in the ARPM.<\/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-bd1a820 elementor-widget elementor-widget-image\" data-id=\"bd1a820\" 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\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2023\/10\/algorithme-kruskal.jpg\" 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-256927d elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"256927d\" 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-scientist-course\">\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\">Training in Data Science<\/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<div class=\"elementor-element elementor-element-cef434a elementor-widget elementor-widget-heading\" data-id=\"cef434a\" 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-medium\">Mathematical translation<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-57b5b77 elementor-widget elementor-widget-text-editor\" data-id=\"57b5b77\" 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>In <a href=\"https:\/\/datascientest.com\/en\/sequences-and-series-understanding-these-two-mathematical-concepts\">mathematical terms<\/a>, the Kruskal algorithm translates as follows:<\/p><p>T = \u00f8<br \/>Sort the a&#8217;s in G by ascending value<br \/>F = { ao }<br \/>Repeat F = { ao } until all S have been included in T<\/p><p>Where<\/p><p>ao : smallest unexamined edge <br \/>T : minimum weight spanning tree <br \/>G : graph<br \/>S : vertex <br \/>p: number of edges already placed in the G graph<br \/>n : number of vertices in graph G<br \/>F = { ao } :addition of the smallest unexamined edge<\/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-0927ed2 elementor-widget elementor-widget-text-editor\" data-id=\"0927ed2\" 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><strong>Good to know:<\/strong> The number of edges in an ARPM can vary by (n-1)n\/2 . The fewer edges the minimum-weight spanning tree contains, the faster the <strong>Kruskal algorithm.<\/strong><\/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-908a650 e-flex e-con-boxed e-con\" data-id=\"908a650\" 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-0e9a171 elementor-widget elementor-widget-heading\" data-id=\"0e9a171\" 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\">Why use the Kruskal algorithm?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-19d4e3f elementor-widget elementor-widget-text-editor\" data-id=\"19d4e3f\" 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>In practice, this<strong> algorithm<\/strong> is often used to solve practical problems such as the design of low-cost communication networks, cabling planning, the elimination of less profitable sea links while preserving accessibility to different ports, and so on.<\/p><p>Whatever the practical application,<strong> Kruskal&#8217;s<\/strong> algorithm enables connections to be optimized. This is precisely why it is so useful in<a href=\"https:\/\/datascientest.com\/en\/boosting-business-with-3-essential-machine-learning-algorithms\"> Machine Learning<\/a>. By optimizing the weight of connections, it maximizes the efficiency of machine learning models.<\/p><p>Good to know: you can use Kruskal&#8217;s algorithm in a variety of programming languages, such as <a href=\"https:\/\/datascientest.com\/en\/c-what-is-this-computer-language-for\">C++<\/a>, Python, Java, C#, Javascript, etc.<\/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-5e7ab04 e-flex e-con-boxed e-con\" data-id=\"5e7ab04\" 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-eee9ab4 elementor-widget elementor-widget-heading\" data-id=\"eee9ab4\" 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\">Deepen your knowledge of Machine Learning with DataScientest<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1f0c24f elementor-widget elementor-widget-text-editor\" data-id=\"1f0c24f\" 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>Beyond the <strong>Kruskal algorithm<\/strong>,<a href=\"https:\/\/datascientest.com\/en\/unraveling-machine-learning-vs-deep-learning-key-differences-explained\"> Machine Learning<\/a> requires mastery of a multitude of mathematical and statistical concepts, not to mention programming languages, <a href=\"https:\/\/datascientest.com\/en\/big-data-for-dummies\">Big Data tools<\/a>, data visualization and more. These are all technical skills that can only be learned through comprehensive training. Like the one offered by DataScientest. Discover our program.<\/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-21c799a elementor-widget elementor-widget-image\" data-id=\"21c799a\" 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\/2023\/10\/algorithme-kruskal1.jpg\" 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-5e53aec elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"5e53aec\" 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-scientist-course\">\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\">Learn to use the algorithm<\/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-d720ac4 e-flex e-con-boxed e-con\" data-id=\"d720ac4\" 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-51f9860 elementor-widget elementor-widget-html\" data-id=\"51f9860\" 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\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [{\n    \"@type\": \"Question\",\n    \"name\": \"https:\/\/datascientest.com\/business-intelligence\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Designed in 1956 by Joseph Kruskal, Kruskal's algorithm is used to find a minimum weight spanning tree (MWST) (also known as a minimum spanning tree (MST) or minimum subtending tree) in a non-oriented, weighted connected graph.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"How does the Kruskal algorithm work?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"To find the minimum-weight spanning tree, Kruskal's algorithm involves the following steps: Sort the edges (a) of the graph (G) by increasing weight. In doing so, the lightest edges are examined first. Start with an empty tree (T). That is, a tree containing no edges; its weight is equal to 0. Its construction is progressive, following these steps. Select edges by ascending weight. Start with the lightest edges. If the addition of an edge does not imply the creation of a cycle in the graph, add it to the tree.  Repeat the operation until all vertices (S) are connected. And this without creating a cycle in the ARPM.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Why use the Kruskal algorithm?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"In practice, this algorithm is often used to solve practical problems such as the design of low-cost communication networks, cabling planning, eliminating the least cost-effective sea links while preserving accessibility to different ports, and so on. Whatever the practical application, Kruskal's algorithm enables connections to be optimized. This is precisely why it is so useful in Machine Learning. By optimizing the weight of connections, it maximizes the efficiency of machine learning models.\"\n    }\n  }]\n}\n<\/script>\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>Kruskal&#8217;s algorithm for optimizing connections within a network is one of the key concepts in Machine Learning. Find out how it works and why it&#8217;s so useful in everyday life. What is the Kruskal algorithm? Designed in 1956 by Joseph Kruskal, Kruskal&#8217;s algorithm is used to find a minimum weight spanning tree (MWST) (also known [&hellip;]<\/p>\n","protected":false},"author":67,"featured_media":182312,"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>Kruskal Algorithm: Definition and Purpose<\/title>\n<meta name=\"description\" content=\"Discover the Kruskal algorithm, a popular algorithm in graph theory used to find the minimum spanning tree of a connected...\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/datascientest.com\/en\/kruskal-algorithm-definition-and-purpose\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Kruskal Algorithm: Definition and Purpose\" \/>\n<meta property=\"og:description\" content=\"Kruskal&#039;s algorithm for optimizing connections within a network is one of the key concepts in Machine Learning. 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