On MySpace Account Spans and Double Pareto-Like Distribution of Friends

In this work we study the activity span of MySpace accounts and its connection to the distribution of the number of friends. The activity span is the time elapsed since the creation of the account until the user´s last login time. We observe exponentially distributed activity spans. We also observe that the distribution of the number of friends over accounts with the same activity span is well approximated by a lognormal with a fairly light tail. These two findings shed light into the puzzling (yet unexplained) inflection point (knee) in the distribution of friends in MySpace when plotted in log-log scale. We argue that the inflection point resembles the inflection point of Reed´s (Double Pareto) Geometric Brownian Motion with Exponential Stopping Times model. We also present evidence against the Dunbar number hypothesis of online social networks, which argues, without proof, that the inflection point is due to the Dunbar number (a theoretical limit on the number of people that a human brain can sustain active social contact with). While we answer many questions, we leave many others open.