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Unformatted text preview: Quantifying social group evolution Supplementary Information SUPPLEMENTARY INFORMATION doi: 10.1038/nature05 670 1 www.nature.com/nature www.nature.com/nature 1 1 Summary of our main results In Fig.1. we show a schematic illustration of our main results concerning the statistical properties of the community evolution in social networks. The basic events that may occur in the life of a community are shown in Fig.1a: a community can grow by recruiting new members, or contract by losing members; two (or more) groups may merge into a single community, while a large enough social group can split into several smaller ones; new communities are born and old ones may disappear. A question of great interest connected to these phenomena is the connection between the expected life-span of a community and its other statistical properties. 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 adapt- ability 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. This effect is illustrated in Fig.1b-e, where we show the time evolution of four communities from the co-authorship network investigated. As Fig.1b. indicates, a typical small and stationary community undergoes minor changes, but lives for a long time. This is well illustrated by the snapshots of the community structure, showing that the communitys stability is conferred by a core of three individuals representing a col- laborative group spanning over 52 months. While new co-authors are added occasionally to the group, they come and go. In contrast, a small community with high turnover of its members, (several members abandon the community at the second time step, followed by three new members joining in at time step three) has a lifetime of nine time steps only (Fig.1c). The opposite is seen for large communities: a large stationary community disintegrates after four time steps (Fig.1d). In contrast, a large non-stationary community whose members change dynamically, resulting in significant fluctuations in both size and the composition, has quite extended lifetime (Fig.1e). Indeed, while the community undergoes dramatic changes, gaining or losing a high fraction of its membership, it can easily withstand these changes. 2 Construction of the networks In our studies the two time dependent networks were constructed from data concerning collabora- tion/communication acts between the people involved. In case of the Los Alamos cond-mat archive , the primary data set contained the monthly roster of articles, (altogether 142 months, over 30000 authors), whereas in case of the phone-call network the phone-calls between the customers were aggregated over two week long periods (altogether 26 periods, over 4 million users). In both cases, we assumed that thetwo week long periods (altogether 26 periods, over 4 million users)....
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- Spring '08