Quantifying social group evolution

Abstract

The rich set of interactions between individuals in the society [1,2,3,4,5,6,7] results in complex community structure, capturing highly connected circles of friends, families, or professional cliques in a social network [3,7,8 [23,24], that allows, for the first time, to investigate the time dependence of overlapping communities on a large scale and as such, to uncover basic relationships characterising community evolution. Our focus is on networks capturing the collaboration between scientists and the calls between mobile phone users. 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. 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 estimating 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 phonecalls 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 (timedependent) links. The extraction of the changing link weights from the primary data is described in the Supplementary Information. 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 and the overlap between communities is very significant, whereas in the phone-call network the communities are less interconnected and are often 1

Collaboration: Group theory

“…And the optimum rate of turnover seems to depend on the size of the team. In a paper published in Nature last year 3 , physicist Gergely Palla of the Hungarian Academy of Sciences in Budapest and his colleagues analysed networks of authorship on physics papers posted to the arXiv preprint server. They showed that teams with around 20 members had a better chance of surviving for a long period if they had a high rate of arrival and departure.…”

Temporal networks

“…The works incorporating a time dimension into the community detection (like Refs. [110,118,132,133]) operate on aggregated timeslices of the temporal network. One can imagine clustering algorithms based on more elaborate temporal structures, like time-respecting paths (a rare exception is Ref.…”

Detecting Community Structure in Dynamic Social Networks Using the Concept of Leadership

“…The other drawback of independent clustering is the computing similarities between huge numbers of the communities across multiple snapshots. Since the number of the found communities of each snapshot could be more than the number of nodes, it could be impractical in facing big dynamic networks like the method introduced in [32]. Apart from independent clustering, evolutionary clustering was introduced.…”