  We study the effects of spatial constraints on the structural properties of
networks embedded in one or two dimensional space. When nodes are embedded in
space, they have a well defined Euclidean distance $r$ between any pair. We
assume that nodes at distance $r$ have a link with probability $p(r) \sim r^{-
\delta}$. We study the mean topological distance $l$ and the clustering
coefficient $C$ of these networks and find that they both exhibit phase
transitions for some critical value of the control parameter $\delta$ depending
on the dimensionality $d$ of the embedding space. We have identified three
regimes. When $\delta <d$, the networks are not affected at all by the spatial
constraints. They are ``small-worlds'' $l\sim \log N$ with zero clustering at
the thermodynamic limit. In the intermediate regime $d<\delta<2d$, the networks
are affected by the space and the distance increases and becomes a power of
$\log N$, and have non-zero clustering. When $\delta>2d$ the networks are
``large'' worlds $l \sim N^{1/d}$ with high clustering. Our results indicate
that spatial constrains have a significant impact on the network properties, a
fact that should be taken into account when modeling complex networks.
