  We consider the domination number for on-line social networks, both in a
stochastic network model, and for real-world, networked data. Asymptotic
sublinear bounds are rigorously derived for the domination number of graphs
generated by the memoryless geometric protean random graph model. We establish
sublinear bounds for the domination number of graphs in the Facebook 100 data
set, and these bounds are well-correlated with those predicted by the
stochastic model. In addition, we derive the asymptotic value of the domination
number in classical random geometric graphs.
