Online Communities: A Longitudinal Analysis of Communication Activities
An interesting study (PDF) from way back discusses how community size and activities reflect the healt of that community. It is from 2003, but in th light of recent social media explosion this isa very useful material.
Another piece of interesting research is Membership Size, Communication Activity, and Sustainability: A Resource-Based Model of Online Social Structures PDF. It is even older than the first one but still has a lot of relevant suff in it.
There is an increasing interest in the factors underljdng the development of online social structures. It has been proposed that these structures are new forms of organizing which are not subject to the same constraints as traditional social structures.
Drawing from prior studies of traditional social structures and empirical analyses of longitudinal data from a sample of Internet-based groups, this exploratory work considers the role of size and communication activity in sustainable online social structures.
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