  The extreme eigenvalues of adjacency matrices are important indicators on the
influences of topological structures to collective dynamical behavior of
complex networks. Recent findings on the ensemble averageability of the extreme
eigenvalue further authenticate its sensibility in the study of network
dynamics. Here we determine the ensemble average of the extreme eigenvalue and
characterize the deviation across the ensemble through the discrete form of
random scale-free network. Remarkably, the analytical approximation derived
from the discrete form shows significant improvement over the previous results.
This has also led us to the same conclusion as [Phys. Rev. Lett. 98, 248701
(2007)] that deviation in the reduced extreme eigenvalues vanishes as the
network size grows.
