  Within a random-matrix-theory approach, we use the nearest-neighbor energy
level spacing distribution $P(s)$ and the entropic eigenfunction localization
length $\ell$ to study spectral and eigenfunction properties (of adjacency
matrices) of weighted random--geometric and random--rectangular graphs. A
random--geometric graph (RGG) considers a set of vertices uniformly and
independently distributed on the unit square, while for a random--rectangular
graph (RRG) the embedding geometry is a rectangle. The RRG model depends on
three parameters: The rectangle side lengths $a$ and $1/a$, the connection
radius $r$, and the number of vertices $N$. We then study in detail the case
$a=1$ which corresponds to weighted RGGs and explore weighted RRGs
characterized by $a\sim 1$, i.e.~two-dimensional geometries, but also approach
the limit of quasi-one-dimensional wires when $a\gg1$. In general we look for
the scaling properties of $P(s)$ and $\ell$ as a function of $a$, $r$ and $N$.
We find that the ratio $r/N^\gamma$, with $\gamma(a)\approx -1/2$, fixes the
properties of both RGGs and RRGs. Moreover, when $a\ge 10$ we show that
spectral and eigenfunction properties of weighted RRGs are universal for the
fixed ratio $r/{\cal C}N^\gamma$, with ${\cal C}\approx a$.
