  In this paper, we investigate the energy of a weighted random graph $G_p(f)$
in $G_{n,p}(f)$, in which each edge $ij$ takes the weight $f(d_i,d_j)$, where
$d_v$ is a random variable, the degree of vertex $v$ in the random graph $G_p$
of the Erd\"{o}s--R\'{e}nyi random graph model $G_{n,p}$, and $f$ is a
symmetric real function on two variables. Suppose $|f(d_i,d_j)|\leq C n^m$ for
some constants $C, m>0$, and $f((1+o(1))np,(1+o(1))np)=(1+o(1))f(np,np)$. Then,
for almost all graphs $G_p(f)$ in $G_{n,p}(f)$, the energy of $G_p(f)$ is
$(1+o(1))f(np,np)\frac{8}{3\pi}\sqrt{p(1-p)}\cdot n^{3/2},$ where $p\in(0,1)$
is any fixed and independent of $n$. Consequently, with this one basket we can
get the asymptotic values of various kinds of graph energies of chemical use,
such as Randi\'c energy, ABC energy, and energies of random matrices obtained
from various kinds of degree-based chemical indices.
