In this work, we use the Havel-Hakimi algorithm to visualize data collected from students to investigate classroom networks. The Havel-Hakimi algorithm uses a recursive method to create a simple graph from a graphical degree sequence. In this case, the degree sequence is a representation of the students in a classroom, and we use the number of peers with whom a student studied or collaborated to determine the degree of each. We expand upon the Havel-Hakimi algorithm by coding a program in MATLAB that generates random graphs with the same degree sequence. Then, we run another algorithm to find the isomorphism classes within the randomly generated graphs. Once we have reduced the problem to the isomorphism classes, we can then choose a graph we think most accurately describes the classroom network. At the end of this work, we will make a note on the rainbow connection number in oriented graphs with diameter 2.
","abstract_html":"<p>In this work, we use the Havel-Hakimi algorithm to visualize data collected from students to investigate classroom networks. The Havel-Hakimi algorithm uses a recursive method to create a simple graph from a graphical degree sequence. In this case, the degree sequence is a representation of the students in a classroom, and we use the number of peers with whom a student studied or collaborated to determine the degree of each. We expand upon the Havel-Hakimi algorithm by coding a program in MATLAB that generates random graphs with the same degree sequence. Then, we run another algorithm to find the isomorphism classes within the randomly generated graphs. Once we have reduced the problem to the isomorphism classes, we can then choose a graph we think most accurately describes the classroom network. At the end of this work, we will make a note on the rainbow connection number in oriented graphs with diameter 2.</p>","abstract_has_math":false,"creators":["Holliday, Rebecca"],"institution":null,"degree_name":"Master of Science in Mathematics (M.S.)","degree_level":"Thesis (open access)","degree_discipline":"Department of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Jonathan Hilpert","Hua Wang"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-01-01T08:00:00Z","date_published":"2015-01-01T08:00:00Z","updated_at":"2026-07-24T02:28:22Z","subjects":["ETD","Graphs","isomorphism","havel hakimi","rainbow","Discrete Mathematics and Combinatorics","Other Applied Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/1284","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jonathan Hilpert","Hua Wang"]},{"key":"dc:creator","label":"Author","values":["Holliday, Rebecca"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2015-04-09T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis (open access)"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics (M.S.)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ETD","Graphs","isomorphism","havel hakimi","rainbow","Discrete Mathematics and Combinatorics","Other Applied Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/1284"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this work, we use the Havel-Hakimi algorithm to visualize data collected from students to investigate classroom networks. The Havel-Hakimi algorithm uses a recursive method to create a simple graph from a graphical degree sequence. In this case, the degree sequence is a representation of the students in a classroom, and we use the number of peers with whom a student studied or collaborated to determine the degree of each. We expand upon the Havel-Hakimi algorithm by coding a program in MATLAB that generates random graphs with the same degree sequence. Then, we run another algorithm to find the isomorphism classes within the randomly generated graphs. Once we have reduced the problem to the isomorphism classes, we can then choose a graph we think most accurately describes the classroom network. At the end of this work, we will make a note on the rainbow connection number in oriented graphs with diameter 2.
"]},{"key":"dc:title","label":"Title","values":["Graphs of Classroom Networks"]}]}],"canonical_facts":{"dc:contributor":["Jonathan Hilpert","Hua Wang"],"dc:creator":["Holliday, Rebecca"],"dc:date.available":["2015-04-09T07:00:00Z"],"dc:description.abstract":["In this work, we use the Havel-Hakimi algorithm to visualize data collected from students to investigate classroom networks. The Havel-Hakimi algorithm uses a recursive method to create a simple graph from a graphical degree sequence. In this case, the degree sequence is a representation of the students in a classroom, and we use the number of peers with whom a student studied or collaborated to determine the degree of each. We expand upon the Havel-Hakimi algorithm by coding a program in MATLAB that generates random graphs with the same degree sequence. Then, we run another algorithm to find the isomorphism classes within the randomly generated graphs. Once we have reduced the problem to the isomorphism classes, we can then choose a graph we think most accurately describes the classroom network. At the end of this work, we will make a note on the rainbow connection number in oriented graphs with diameter 2.
"],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/1284"],"dc:subject":["ETD","Graphs","isomorphism","havel hakimi","rainbow","Discrete Mathematics and Combinatorics","Other Applied Mathematics"],"dc:title":["Graphs of Classroom Networks"],"thesis:degree_discipline":["Department of Mathematical Sciences"],"thesis:degree_level":["Thesis (open access)"],"thesis:degree_name":["Master of Science in Mathematics (M.S.)"]},"updated_at":"2026-07-24T02:28:22Z"}