  Let $n$ and $a$ be positive integers such that $2\leq a\leq \frac{n}{2}$. In
this short note, we compute for the exact value of the distance spectral
radius, vertex-forwarding index, and some distance-based topological indices of
the complement of circulant networks $C_n(1,a)$ and
$C_{m^h}(1,m,m^2,\ldots,m^{h-1})$. For $a\neq \frac{n}{2}$, the circulant
$C_n(1,a)$ is called a double loop network while the circulant
$C_{m^h}(1,m,m^2,\ldots,m^{h-1})$ is called the multiplicative circulant
network on $m^h$ vertices.
