The hyperbolic model can be used to model time-evolving communities. The behaviour of the core size and tail thickness over time will describe the changing dynamics of the communities; for instance, if the core gets (relatively) smaller as the community grows, that would indicate sparcification within the community.
In [1], we study the behaviour of on-line question-answer communities over time. We study various Stack Exhange communities, as well as HealthBoards and Reddit communities. Surprisingly, it turns out that they generally have a core size that stays a constant fraction of the community size; typically the core is between 10 and 20 % of the community. In these communities the core corresponds to those users that are active in answering questions and commenting answers and questions, and the constant size of the core seems to indicate behaviour similar to that of the famous Pareto principle.
References
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Stability and dynamics of communities on online question-answer sites.
Social Networks
58,
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50–58.
10.1016/j.socnet.2018.12.004
[pdf (Elsevier) | more information]