Connectivity distribution and attack tolerance of general networks with both preferential and random attachments

A general class of growing networks is constructed with both preferential and random attachments, which includes random and scale-free networks as limiting cases when a physical parameter is tuned. Formulas are derived characterizing the evolution and distribution of the connectivity, which are verified by numerical computations. Study of the effect of random failures and intentional attacks on the performance of network suggests that general networks which are neither completely random nor scale-free are desirable.