Online social networks pose significant challenges to computer scientists, physicists, and sociologists alike, for their massive size, fast evolution, and uncharted potential for social computing. One particular problem that has interested us is community identification. Many algorithms based on various metrics have been proposed for communities in networks [18, 24], but a few algorithms scale to very large networks. Three recent community identification algorithms, namely CNM [16], Wakita [59], and Louvain [10], stand out for their scalability to a few millions of nodes. All of them use modularity as the metric of optimization. However, all three algorithms produce inconsistent communities every time the ordering of nodes to the algorithms changes.

Online social networking services are among the most popular Internet services according to Alexa.com and have become a key feature in many Internet services. Users interact through various features of online social networking services: making friend relationships, sharing their photos, and writing comments. These friend relationships are expected to become a key to many other features in web services, such as recommendation engines, security measures, online search, and personalization issues. However, we have very limited knowledge on how much interaction actually takes place over friend relationships declared online. A friend relationship only marks the beginning of online interaction.