Facebook as a Small World: a topological hypothesis

Abstract

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 evolutionary 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 concept 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.