  By constructing a multicanonical Monte Carlo simulation, we obtain the full
probability distribution $\rho_N(r)$ of the degree assortativity coefficient
$r$ on configuration networks of size $N$ by using the multiple histogram
reweighting method. We suggest that $\rho_N(r)$ obeys a large deviation
principle, $\rho_N \left(r-r_N^* \right) \asymp {e^{ - {N^\xi }I\left( {r-
r_N^* } \right)}}$, where the rate function $I$ is convex and possesses its
unique minimum at $r=r_N^*$, and $\xi$ is an exponent that scales $\rho_N$'s
with $N$. We show that $\xi=1$ for Poisson random graphs, and $\xi\geq1$ for
scale-free networks in which $\xi$ is a decreasing function of the degree
distribution exponent $\gamma$. Our results reveal that the fluctuations of $r$
exhibits an anomalous scaling with $N$ in highly heterogeneous networks.
