Using Graph Theory to Analyze Drama
A graph showing betweenness of nodes. For the characters in your favorite play, what is the betweeness centrality, or measure of importance based on the frequency of communication between each of them?Copyright 2007 (top) Claudio Rocchini, Wikipedia Commons; (bottom) National Endowment for the Arts http://commons.wikimedia.org/wiki/File:Graph_betweenness.svg http://www.nea.gov/national/shakespeare/Photos.html
Students analyze dramatic works using graph theory. They gather data, record it in Microsoft Excel and use Cytoscape (a free, downloadable application) to generate graphs that visually illustrate the key characters (nodes) and connections between them (edges). The nodes in the Cytoscape graphs are color-coded and sized according to the importance of the node (in this activity nodes represent characters in the work and their relative importance to the story). After the analysis, the graphs are further examined to see what the visual depiction of the story in the form of a graph tells readers about the inner workings of the dramatic work. Students gain practice with graph theory vocabulary, including node, edge, betweeness centrality and degree on interaction, and learn about a range of engineering applications of graph theory.
The mathematical structures of graph theory are widely applied in computer science, mathematics and engineering to model relationships between objects in sets of objects.
Software engineers use graphs to represent communication networks, data organization, computational devices, the flow of computation and more. They also exploit the relationships documented in social networks on websites like Facebook to market products to consumers. And they use graph theory to represent website structures, with the vertices being web pages and the edges being links between pages.
Electrical engineers and computer electronic engineers employ graph theory in the design of integrated circuits. Complex layered microcircuits can be represented as nodes interconnected by lines or arcs. The use of graph theory helps engineers optimize the density of components and minimize the connections, which optimizes processing speed and electrical efficiency.
After this activity, students should be able to:
- Apply graph theory to dramatic works of literature.
- Use Microsoft Excel and Cytoscape to develop graphs of dramatic works of literature.
- Analyze graphs to determine the importance of characters and the quality (subtlety) of communication between characters of dramatic works of literature.
- Create a social graph for a dramatic text.
- Derive meaning from the graphs they have created and craft an essay explaining the results.