Quantitative social group dynamics on a large scale

The rich set of interactions between individuals in the society [1, 2, 3, 4, 5, 6] results in complex community structure, capturing highly connected circles of friends, families, or professional cliques in a social network [3, 7, 8, 9, 10]. Although most empirical studies have focused on snapshots of these communities, thanks to frequent changes in the activity and communication patterns of individuals, the associated social and communication network is subject to constant evolution [6, 11, 12, 13, 14, 15, 16]. Our knowledge of the mechanisms governing the underlying community dynamics is limited, but is essential for a deeper understanding of the development and selfoptimisation of the society as a whole [17, 18, 19, 20, 21, 22]. We have developed a new algorithm based on a clique percolation technique [23, 24], that allows, for the first time, to investigate in detail the time dependence of overlapping communities on a large scale and as such, to uncover basic relationships of the statistical features of community evolution. Our focus is on two networks of major interest, capturing the collaboration between scientists and the calls between mobile phone users, observing that their communities are subject to a number of elementary evolutionary steps ranging from community formation to breakup and merging, representing new dimensions in their quantitative interpretation. We find that large groups persist longer if they are capable of dynamically altering their membership, suggesting that an ability to change the composition results in better adaptability and a longer lifetime for social groups. Remarkably, the behaviour of small groups displays the opposite tendency, the condition for stability being that their composition remains unchanged. We also show that the knowledge of the time commitment of the members to a given community can be used for predicting the community’s lifetime. These findings offer a new view on the fundamental differences between the dynamics of small groups and large institutions. The data sets we consider contain the monthly roster of articles in the Los Alamos cond-mat archive spanning 142 months, with over 30000 authors [25], and the complete record of phone-calls between the customers of a mobile phone company spanning 52 weeks (accumulated over two week long periods), and containing the communication patterns of over 4 million users. Both type of collaboration events (a new article or a phone-call) document the presence of social interaction between the involved individuals (nodes), and can be represented as (time-dependent) links. The extraction of the changing link weights from the primary data is described in the Supplementary Material. In Fig.1a-b we show the local structure at a given time step in the two networks in the vicinity of a randomly chosen individual (marked by a red frame). The communities (social groups represented by more densely interconnected parts within a network of social links) are colour coded, so that black nodes/edges do not belong to any community, and those that simultaneously belong to two or more communities are shown in red. The two networks have rather different local structure: due to its bipartite nature, the collaboration network is quite dense