{"id":1194,"date":"2017-01-24T01:51:23","date_gmt":"2017-01-24T01:51:23","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/?post_type=chapter&#038;p=1194"},"modified":"2019-05-30T16:32:01","modified_gmt":"2019-05-30T16:32:01","slug":"why-it-matters-graph-theory","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/chapter\/why-it-matters-graph-theory\/","title":{"raw":"Why It Matters: Graph Theory","rendered":"Why It Matters: Graph Theory"},"content":{"raw":"<h2>Why understand graph theory?<\/h2>\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/28195124\/briefcase.jpg\"><img class=\"wp-image-2312 alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/28195124\/briefcase-300x200.jpg\" alt=\"Silhouette of a businessman running with briefcase in hand against a dark background\" width=\"354\" height=\"236\" \/><\/a>You shined your shoes and packed your briefcase. \u00a0Now it\u2019s time to stop in at each of your clients now that you are the main sales representative for your company. \u00a0You have nine clients in the same region, and you have mapped them out by determining the time it will take you to get from one to the other in minutes. \u00a0You labeled the clients A through I, and your original plan was to visit them in alphabetical order. \u00a0Sounds easy enough. \u00a0The problem is that when you finish up with client G, you realize you left a very important sample back at Client C. \u00a0How can you determine the shortest path back? \u00a0And then once you get it, how can you decide the fastest route to your next client?\r\n\r\n&nbsp;\r\n\r\nYou can start by making a diagram showing the travel time\u00a0between each client. \u00a0However, there are multiple paths that are possible from any one client to another. Your diagram looks a bit overwhelming - it\u00a0isn\u2019t immediately\u00a0obvious which route would be the fastest.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/28195356\/graphtheory.png\"><img class=\"wp-image-2315 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/28195356\/graphtheory-300x216.png\" alt=\"Graph diagram connects locations A through E. A connects to B by 8 units, B to C by 8 units, C to D by 10 units, D to E by 8 units, E to F by 7 units, F to G by 5 units, G to H by 5 units, and H to I by 5 units. In addition, B connects to D by 14 units, B to F by 20 units, F to I by 15 units, and G to I by 12 units.\" width=\"521\" height=\"375\" \/><\/a>\r\n\r\n&nbsp;\r\n\r\nFortunately, you\u2019ll learn how to solve the problem as you complete this module. \u00a0You will figure out how to interpret diagrams such as this and use them to make logical decisions, such as which way to go to keep your clients happy and close the deal.\r\n","rendered":"<h2>Why understand graph theory?<\/h2>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/28195124\/briefcase.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-2312 alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/28195124\/briefcase-300x200.jpg\" alt=\"Silhouette of a businessman running with briefcase in hand against a dark background\" width=\"354\" height=\"236\" \/><\/a>You shined your shoes and packed your briefcase. \u00a0Now it\u2019s time to stop in at each of your clients now that you are the main sales representative for your company. \u00a0You have nine clients in the same region, and you have mapped them out by determining the time it will take you to get from one to the other in minutes. \u00a0You labeled the clients A through I, and your original plan was to visit them in alphabetical order. \u00a0Sounds easy enough. \u00a0The problem is that when you finish up with client G, you realize you left a very important sample back at Client C. \u00a0How can you determine the shortest path back? \u00a0And then once you get it, how can you decide the fastest route to your next client?<\/p>\n<p>&nbsp;<\/p>\n<p>You can start by making a diagram showing the travel time\u00a0between each client. \u00a0However, there are multiple paths that are possible from any one client to another. Your diagram looks a bit overwhelming &#8211; it\u00a0isn\u2019t immediately\u00a0obvious which route would be the fastest.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/28195356\/graphtheory.png\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-2315 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/28195356\/graphtheory-300x216.png\" alt=\"Graph diagram connects locations A through E. A connects to B by 8 units, B to C by 8 units, C to D by 10 units, D to E by 8 units, E to F by 7 units, F to G by 5 units, G to H by 5 units, and H to I by 5 units. In addition, B connects to D by 14 units, B to F by 20 units, F to I by 15 units, and G to I by 12 units.\" width=\"521\" height=\"375\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n<p>Fortunately, you\u2019ll learn how to solve the problem as you complete this module. \u00a0You will figure out how to interpret diagrams such as this and use them to make logical decisions, such as which way to go to keep your clients happy and close the deal.<\/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-1194\">\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>Why It Matters: Graph Theory. <strong>Authored 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><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Businessman silhouette. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/pixabay.com\/en\/man-silhouette-businessman-escape-1675685\">https:\/\/pixabay.com\/en\/man-silhouette-businessman-escape-1675685<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/cc0\">CC0: No Rights Reserved<\/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":1,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Why It Matters: Graph Theory\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Businessman silhouette\",\"author\":\"\",\"organization\":\"\",\"url\":\"https:\/\/pixabay.com\/en\/man-silhouette-businessman-escape-1675685\",\"project\":\"\",\"license\":\"cc0\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"047c0561-dd6c-461a-8ab1-481920e0c38e","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1194","chapter","type-chapter","status-publish","hentry"],"part":1193,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/1194","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":11,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/1194\/revisions"}],"predecessor-version":[{"id":2961,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/1194\/revisions\/2961"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/parts\/1193"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/1194\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/media?parent=1194"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapter-type?post=1194"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/contributor?post=1194"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/license?post=1194"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}