{"id":1073,"date":"2017-01-11T00:40:32","date_gmt":"2017-01-11T00:40:32","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/?post_type=chapter&#038;p=1073"},"modified":"2017-04-18T18:34:57","modified_gmt":"2017-04-18T18:34:57","slug":"introduction-graph-theory","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/chapter\/introduction-graph-theory\/","title":{"raw":"Introduction: Graph Theory Basics","rendered":"Introduction: Graph Theory Basics"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\nIn this lesson you will learn how to:\r\n<ul>\r\n \t<li>Identify the vertices, edges, and loops of a graph<\/li>\r\n \t<li>Identify the degree of a vertex<\/li>\r\n \t<li>Identify and draw both a path and a circuit through a graph<\/li>\r\n \t<li>Determine whether a graph is connected or disconnected<\/li>\r\n \t<li>Find the shortest path through a graph using Dijkstra's Algorithm<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\nIn this lesson, we will introduce Graph Theory, a field of mathematics that started approximately 300 years ago to help solve problems such as finding the shortest path between two locations.\r\n\r\nNow, elements of graph theory are used to optimize a wide range of\u00a0systems, generate friend suggestions on social media, and plan complex shipping and air traffic routes.\r\n","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<p>In this lesson you will learn how to:<\/p>\n<ul>\n<li>Identify the vertices, edges, and loops of a graph<\/li>\n<li>Identify the degree of a vertex<\/li>\n<li>Identify and draw both a path and a circuit through a graph<\/li>\n<li>Determine whether a graph is connected or disconnected<\/li>\n<li>Find the shortest path through a graph using Dijkstra&#8217;s Algorithm<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<br \/>\nIn this lesson, we will introduce Graph Theory, a field of mathematics that started approximately 300 years ago to help solve problems such as finding the shortest path between two locations.<\/p>\n<p>Now, elements of graph theory are used to optimize a wide range of\u00a0systems, generate friend suggestions on social media, and plan complex shipping and air traffic routes.<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1073\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Learning Outcomes. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li><strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":21,"menu_order":2,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Learning Outcomes\",\"author\":\"\",\"organization\":\"Lumen 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