Identifying Sociological Patterns in Facebook Networks (2008)

Undergraduate: Amanda Traud

Faculty Advisor: Peter Mucha
Department: Mathematics

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Arising in biology, physics, technology, and the social sciences, networks typically share properties with structured and random graphs. Most networks can be decomposed into "communities” with more connections inside communities than across them. With real-world social connections spilling over into the digital domain, online social networks provide information about underlying real world ties. Using variants of eigenvector-based methods for community detection [M. Newman, Phys. Rev. E 74, 036104 (2006)], we identify communities of pages/individuals in Facebook networks restricted to individual schools (ignoring cross-school links), approximately optimizing the “modularity” of partition, defined in terms of the number of intra-community edges compared to that expected in a random network with the same degree distribution. We use the identified communities to better understand the sociological structure of the network by comparing against a collection of characteristics provided by each individual page owner, e.g., the clustering of Caltech-affiliated Facebook pages correlates well with the residential "Houses." We quantify this comparison by correlation coefficients between the algorithm-given communities and the self-selected characteristics. We additionally identify communities in corresponding gender-restricted networks, comparing with the overall networks and characteristics, and investigate communities in the Facebook networks of other colleges and universities.