Finding hierarchy in directed online social networks

Social hierarchy and stratification among humans is a well studied concept in sociology. The popularity of online social networks presents an opportunity to study social hierarchy for different types of networks and at different scales. We adopt the premise that people form connections in a social network based on their perceived social hierarchy; as a result, the edge directions in directed social networks can be leveraged to infer hierarchy. In this paper, we define a measure of hierarchy in a directed online social network, and present an efficient algorithm to compute this measure. We validate our measure using ground truth including Wikipedia notability score. We use this measure to study hierarchy in several directed online social networks including Twitter, Delicious, YouTube, Flickr, LiveJournal, and curated lists of several categories of people based on different occupations, and different organizations. Our experiments on different online social networks show how hierarchy emerges as we increase the size of the network. This is in contrast to random graphs, where the hierarchy decreases as the network size increases. Further, we show that the degree of stratification in a network increases very slowly as we increase the size of the graph.