s . so c - ph ] 2 4 A ug 2 01 4 1 Empirical studies on the network of social groups : the case of Tencent QQ

Participation in social groups are important but the collective behaviors of human as a group are difficult to analyze due to the difficulties to quantify ordinary social relation, group membership, and to collect a comprehensive dataset. Such difficulties can be circumvented by analyzing online social networks. In this paper, we analyze a comprehensive dataset obtained from Tencent QQ, an instant messenger with the highest market share in China. Specifically, we analyze three derivative networks involving groups and their members – the hypergraph of groups, the network of groups and the user network – to reveal social interactions at microscopic and mesoscopic level. Our results uncover interesting behaviors on the growth of user groups, the interactions between groups, and their relationship with member age and gender. These findings lead to insights which are difficult to obtain in ordinary social networks. Introduction Social interactions are essential to us, yet our understanding on their collective behaviors is limited. Major reasons include the difficulties to quantify individual social relationship and to collect a comprehensive dataset. Nevertheless, the rapid development of the Internet has revolutionize the form of social interactions from postal mails, telephone voice calls, physical meeting and gathering, to emails, instant messaging, online forum and online social networks. Through the internet, interactions are quantified into data which greatly facilitates the studies of social networks. Many exciting findings are revealed. As an example, the hypothesis of six degrees of separation was initialized in 1930s [1], which states that any two person can be connected to by a small number of acquaintances, was only recently tested on Facebook network which gives an average degree of separation of roughly 4 [2]. Other features revealed on online social networks include power-law degree distribution [3], community structure [4,5] and special communication patterns [6–8]. So far the studies on online social networks focus mainly on individual social relationship, leaving another important aspect – participation in social groups – less understood. It is because the collective behavior of human as a group is difficult to study in ordinary social networks due to the ambiguity in quantitatively affiliating individuals to specific groups. This problem does not occur on the Internet since group-based applications have a definite membership identity for individuals. For instance, prototype online applications such as chatrooms and bulletin board systems (BBS) involve individual users joining and posting messages where membership identity is well defined [9, 10]. These applications set the basis for existing social applications and instant messengers include Windows Live and Google messengers, Whatsapp, Skype, Fetion and Tencent QQ.In these applications, users create social groups on demand and lead to social networks which are more extensive and complicated than their physical counterparts. Two different types of online social groups can be formed on the Internet. The first one is similar to ordinary social networks, which are joined by friends with real personal relationship. Circles in Google plus, Skype and Whatsapp groups belong to this type [11]. The second one is more unique to online social networks, consisting of groups of individuals with common interests but without prior personal