Statistical properties and attack tolerance of growing networks with algebraic preferential attachment

We consider growing networks with algebraic preferential attachment and address two questions: (1) what is the effect of temporal fluctuations in the number of new links acquired by the network? and (2) what is the network tolerance against random failures and intentional attacks? We find that the fluctuations generally have little effect on the network properties, although they lead to a plateau behavior for small degrees in the connectivity distribution. Formulas are derived for the evolution and distribution of the network connectivity, which are tested by numerical simulations. Numerical study of the effect of failures and attacks suggests that networks constructed under algebraic preferential attachment are more robust than scale-free networks.