Comparing community structure to characteristics in online collegiate social networks

We study the structure of social networks of students by examining the graphs of Facebook "friendships" at five U.S. universities at a single point in time. We investigate the community structure of each single-institution network and employ visual and quantitative tools, including standardized pair-counting methods, to measure the correlations between the network communities and a set of self-identified user characteristics (residence, class year, major, and high school). We review the basic properties and statistics of the employed pair-counting indices and recall, in simplified notation, a useful formula for the z-score of the Rand coefficient. Our study illustrates how to examine different instances of social networks constructed in similar environments, emphasizes the array of social forces that combine to form "communities," and leads to comparative observations about online social structures, which reflect offline social structures. We calculate the relative contributions of different characteristics to the community structure of individual universities and compare these relative contributions at different universities. For example, we examine the importance of common high school affiliation at large state universities and the varying degrees of influence that common major can have on the social structure at different universities. The heterogeneity of the communities that we observe indicates that university networks typically have multiple organizing factors rather than a single dominant one. © 2011 Society for Industrial and Applied Mathematics.