On the Rise and Fall of Online Social Networks
  The rise and fall of online social networks recently generated an enormous amount of interest among people, both inside and outside of academia. Gillette [Businessweek magazine, 2011] did a detailed analysis of MySpace, which started losing its popularity since 2008. Cannarella and Spechler [ArXiv, 2014] used a model of disease spread to explain the rise and fall of MySpace. In this paper, we present a graph theoretical model that may be able to provide an alternative explanation for the rise and fall of online social networks. Our model is motivated by the well-known Barabasi-Albert model of generating random scale-free networks using preferential attachment or `rich-gets-richer' phenomenon. As shown by our empirical analysis, we conjecture that such an online social network growth model is inherently flawed as it fails to maintain the stability of such networks while ensuring their growth. In the process, we also conjecture that our model of preferential attachment also exhibits scale-free phenomenon. 
Arnab Basu, Saswata Shannigrahi, Simrat Singh Chhabra, Ajit   Brundavanam
cs.SI physics.soc-ph