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Abstract
Small world networks permeate modern society. Paradoxically, the ubiquity of small world networks is matched only by the difficulty of finding tractable examples. Until we have an extensive taxonomy of small world networks at our disposal, intractability will prevail. In this thesis, we present a methodology for creating and analyzing a practically limitless number of networks exhibiting small world network properties. That is, we analyze networks, the vertices being Facebook groups sharing a common word in the group name and the links being mutual members in any two groups. Specifically, by analyzing the characteristics of single networks and network ensembles, we attempt to quantify how the small world properties scale with network size, and distill the essence of the networks to gain a deeper understanding of the essential features based on insight gained from empirical observation. We show that Facebook group networks have large clustering coefficients that do not vanish with increased network size, and small average path lengths, thus exhibiting small world features. At the same time, the average connectivity increases as a power of the network size, while the average clustering coefficients and average path lengths do not exhibit a clear scaling with the size of the network. Our results are similar to what have been found analyzing the Facebook network proper and give cause to pursue a more in-depth investigation.
