Facebook as a Small World: a topological hypothesis

Facebook is becoming a pervasive entity as its social, cultural and media ramifications grow deep and entrenched in our daily life. Its nature of a complex system of interactions, bearing a strong similarity to networks built through individual choices and systems shaped by evolu- tionary pressure, makes it an interesting target for research. Scale-free Small World networks, recently popularized by Barabasi, are a topological class pertaining to both these domains, whose members have resilience to disruption and short intermediate connections between nodes. In this paper we show that the topological structure of a specific subset of Facebook, gathered using data from a self-report online questionnaire on its usage, is similar but measurably different from a scale-free Small World network. We conjecture that the reason for this counterintuitive result lies in the dynamics behind friendship requests. This con- cept may be extendable to the whole network and to other social networks, and is useful to understand Facebook strengths and weaknesses, and to forecast its evolution.