Asee peer logo

Using Havel-Hakimi to Graph Classroom Networks

Download Paper |


2015 ASEE Annual Conference & Exposition


Seattle, Washington

Publication Date

June 14, 2015

Start Date

June 14, 2015

End Date

June 17, 2015





Conference Session

Examining Social Ties and Networks

Tagged Division

Educational Research and Methods

Page Count


Page Numbers

26.1666.1 - 26.1666.7



Permanent URL

Download Count


Request a correction

Paper Authors


Jonathan C. Hilpert Georgia Southern University

visit author page

Jonathan C. Hilpert is an Educational Psychologist at Georgia Southern University.

visit author page


Rebecca Holliday Georgia Southern University

visit author page

Bachelor of Science in Applied Mathematics from Middle Georgia State College. Currently a graduate student in the Department of Mathematical Sciences at Georgia Southern University with a concentration in Applied Mathematics and research in Graph Theory.

visit author page

Download Paper |


Using Havel-Hakimi to graph classroom networksEngineering education research and ABET accreditation standards both emphasize theimportance of collaborative learning. Researchers have argued that classroomcollaborations can be studied as emergent systems, where the actions of individual agentsproduce an outcome that is not reducible to its individual parts. The underlying structureof an emergent system is a network. Networks can be graphically represented asinterconnected collections of nodes and edges, or in the context of the current studystudents working together in classrooms to learn and solve problems. Althoughresearchers have examined collaborative emergent systems in classrooms from aqualitative perspective, there is need for more advanced tools to examine how thenetwork structure of classrooms influences student learning and performance.In this paper, we use the Havel-Hakimi algorithm to visualize data collected fromstudents to investigate classroom networks. The Havel-Hakimi algorithm uses a recursivemethod to create a simple graph from a graphical degree sequence. In this case, thedegree sequence is a representation of each student in a classroom, and we use thenumber of peers with which a student studied or collaborated to determine the degree.We expand upon the Havel-Hakimi algorithm by coding a program in Python thatgenerates random graphs with the same degree sequence. In doing this, we can examineall potential possibilities of which students work with whom. Then, we use an edge-weight technique to determine which of those random graphs is the best fit to the real lifenetwork in the classroom. Once best fit has been determined, we analyze why theclassroom network looks this way and what it means. To do this, we use Gephi (popularnetwork analysis software) to calculate closeness, betweenness, and other significantmeasures of network characteristics.Our results will describe a useful technique for developing classroom graphs that canaccurately, graphically represent engineering classroom networks. We will show someexample graphs and conclude with a discussion of how these graphs may be related tostudent learning.

Hilpert, J. C., & Holliday, R. (2015, June), Using Havel-Hakimi to Graph Classroom Networks Paper presented at 2015 ASEE Annual Conference & Exposition, Seattle, Washington. 10.18260/p.25002

ASEE holds the copyright on this document. It may be read by the public free of charge. Authors may archive their work on personal websites or in institutional repositories with the following citation: © 2015 American Society for Engineering Education. Other scholars may excerpt or quote from these materials with the same citation. When excerpting or quoting from Conference Proceedings, authors should, in addition to noting the ASEE copyright, list all the original authors and their institutions and name the host city of the conference. - Last updated April 1, 2015