2 research outputs found
Structural properties of spatially embedded networks
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 between any pair. We
assume that nodes at distance have a link with probability . We study the mean topological distance and the clustering
coefficient of these networks and find that they both exhibit phase
transitions for some critical value of the control parameter depending
on the dimensionality of the embedding space. We have identified three
regimes. When , the networks are not affected at all by the spatial
constraints. They are ``small-worlds'' with zero clustering at
the thermodynamic limit. In the intermediate regime , the networks
are affected by the space and the distance increases and becomes a power of
, and have non-zero clustering. When the networks are
``large'' worlds 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.Comment: 5 pages, To appear in Europhysics Letter