  A generalization of the random geometric graph (RGG) model is proposed by
considering a set of points uniformly and independently distributed on a
rectangle of unit area instead of on a unit square [0,1]^2. The topological
properties of the random rectangular graphs (RRGs) generated by this model are
then studied as a function of the rectangle sides lengths a and b=1/a, and the
radius r used to connect the nodes. When a=1 we recover the RGG, and when
a-->infinity the very elongated rectangle generated resembles a one-dimensional
RGG. We obtain here analytical expressions for the average degree, degree
distribution, connectivity, average path length and clustering coefficient for
RRG. These results provide evidence that show that most of these properties
depend on the connection radius and the side length of the rectangle, usually
in a monotonic way. The clustering coefficient, however, increases when the
square is transformed into a slightly elongated rectangle, and after this
maximum it decays with the increase of the elongation of the rectangle. We
support all our findings by computational simulations that show the goodness of
the theoretical models proposed for RRGs.
