A fascinating look at five online communities with a focus on how Friendster died.. from the arXiv (a wee bit technical). Clearly a work in progress, but very interesting to those who follow these things. The bonds between users in Friendster weren't particularly strong and many of the users with a small number of blonds became isolated when their primary bonds broke causing the network to unravel quickly. The authors describe "K-cores" a subset of users who have a lot of connections, but also a degree of resilience and influence. When these started breaking the social network quickly collapsed.
Social Resilience in Online Communities: The Autopsy of Friendster
We empirically analyze five online communities: Friendster, Livejournal, Facebook, Orkut, Myspace, to identify causes for the decline of social networks. We define social resilience as the ability of a community to withstand changes. We do not argue about the cause of such changes, but concentrate on their impact. Changes may cause users to leave, which may trigger further leaves of others who lost connection to their friends. This may lead to cascades of users leaving. A social network is said to be resilient if the size of such cascades can be limited. To quantify resilience, we use the k-core analysis, to identify subsets of the network in which all users have at least k friends. These connections generate benefits (b) for each user, which have to outweigh the costs (c) of being a member of the network. If this difference is not positive, users leave. After all cascades, the remaining network is the k-core of the original network determined by the cost-to-benefit c/b ratio. By analysing the cumulative distribution of k-cores we are able to calculate the number of users remaining in each community. This allows us to infer the impact of the c/b ratio on the resilience of these online communities. We find that the different online communities have different k-core distributions. Consequently, similar changes in the c/b ratio have a different impact on the amount of active users. As a case study, we focus on the evolution of Friendster. We identify time periods when new users entering the network observed an insufficient c/b ratio. This measure can be seen as a precursor of the later collapse of the community. Our analysis can be applied to estimate the impact of changes in the user interface, which may temporarily increase the c/b ratio, thus posing a threat for the community to shrink, or even to collapse.
from the Discussion:
In this article, we have presented the first empirical analysis of social resilience in OSN. We approached this question using a theoretical model that relates the environment of the OSN with the cascades of user departures. We showed how a generalized version of the k-core decomposition allows the empirical measurement of resilience in OSN.
We provided an empirical study of social resilience across five influential OSN, including successful ones like Facebook and unsuccessful ones like Friendster. We have shown that the hypothesis of a power-law degree distribution cannot be accepted for any of these communities, discarding the epidemic properties of complex networks as a possible explanation for large-scale cascades of user departures. Our k-core analysis overcomes this limitation, quantifying social resilience as a collective phenomenon using the CCDF of node coreness. We found that the topologies of two successful sites, Livejournal and Facebook, are less resilient than the unsuccessful Friendster and Orkut. This indicates that the environmental condition of an OSN play a major role for its success. Thus, we conclude that the topology of the social network alone cannot explain the stories of success and failure of the studied OSN, and it is necessary to focus future empirical analysis in measuring these costs and benefits. Additionally, we found very high maximum coreness numbers for most of the OSN we studied. The existence of these superconnected cores indicates that information can be spread efficiently through these OSN .
As a case study, we provided a detailed post hoc analysis of the changes in Friendster through time. We detect that the range of connections towards future nodes is much lower than the expectation from a random process. Using the coreness of the nodes, we could track the time dependence of the risk of leaving for new users. We found shocks that indicate periods of lower resilience of the whole community. Finally, we apply all our findings to Friendster’s collapse, fitting an approximated time series of active users through the spread of user departures predicted by the k-core decomposition. We estimated the amount of active users through search volumes, but other sources can provide more reliable data, like Alexa ranks, or last login times if provided by the site. Such datasets would allow further validations of the k-core decomposition as a measure of social resilience.
Our analysis focused on the macroscopic resilience of OSN, but additional research is necessary to complete our findings. Microscopic data on user activity and churn can provide estimators for the benefits and costs of each network, to further validate the work presented here. Furthermore, the generalized k-core can be applied when user decisions are more complex than just staying or leaving the network, for example introducing heterogeneity of benefits or weights in the social links.
Another open question is the role of directionality in the social network, and how to measure resilience when asymmetric relations are allowed. The benefits of users of these networks would be multidimensional, representing both the reputation of a user and the amount of information it receives from its neighborhood. The work presented here is theoretically limited to the study of monotonously increasing, convex objective functions of benefit versus active neighborhood. While empirical studies support this assumption [4, 30], it is possible to imagine a scenario where information overload decreases the net benefit of users with very large neighborhoods, creating nonlinearities where the generalized k-core is not a stable solution. We leave this questions open for further research, and the study of social resilience in other types of online communities.