Preferential attachment is a popular generative mechanism to
explain the widespread observation of power law-distributed
networks. An alternative explanation for the phenomenon is a
randomly grown network with large individual variation in
growth rates among the nodes (frailty). We derive
analytically the distribution of individual rates, which
will reproduce the connectivity distribution that is
obtained from a general preferential attachment process
(Yule process), and present a statistical test to
distinguish the two generative mechanisms from each other.
We apply the test to two data sets of scientific citation
and sexual partner networks. The findings from the latter
analyses argue for frailty effects as an important mechanism
underlying the dynamics of complex networks.