Graphing Your Social Network
This graph shows the concept of six degrees of separation, the idea that everyone is no more than six "steps" away from each person on Earth. What does your social network look like?Copyright 2007 (top) Laurens van Lieshout, Wikimedia Commons; (bottom) U.S. Department of the Interior http://commons.wikimedia.org/wiki/File:Six_degrees_of_separation_01.png http://www.doi.gov/letsmove/indiancountry/about-us.cfm
Students analyze their social networks using graph theory. They gather data on their own social relationships, either from Facebook interactions or the interactions they have throughout the course of a day, recording it in Microsoft Excel and using Cytoscape (a free, downloadable application) to generate social network graphs that visually illustrate the key persons (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 are people in students' social networks). After the analysis, the graphs are further examined to see what can be learned from the visual representation. 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 their social networks.
- Use Microsoft Excel and Cytoscape to develop graphs of their social networks.
- Analyze their own social network graphs to determine who is connected (more connections to people show importance of relationships/who has the most interactions) and which friends they interact with the most.
- Practice the application of graph theory by charting personal social networks.