  Mean-field analysis is an important tool for understanding dynamics on
complex networks. However, surprisingly little attention has been paid to the
question of whether mean-field predictions are accurate, and this is
particularly true for real-world networks with clustering and modular
structure. In this paper, we compare mean-field predictions to numerical
simulation results for dynamical processes running on 21 real-world networks
and demonstrate that the accuracy of the theory depends not only on the mean
degree of the networks but also on the mean first-neighbor degree. We show that
mean-field theory can give (unexpectedly) accurate results for certain dynamics
on disassortative real-world networks even when the mean degree is as low as 4.
