Year: 2008
Type: article
Abstract: 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 )∼ r −δ . 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 δ depending on the dimensionality d of the embedding space. We have identified three regimes. When δ< d , the networks are not affected at all by the spatial constraints. They are “small-worlds” l ∼log N with zero clustering at the thermodynamic limit. In the intermediate regime d <δ<2 d , the networks are affected by the space and the distance increases and becomes a power of log N , and have non-zero clustering. When δ>2 d the networks are “large” worlds l ∼ 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.
Source: Europhysics Letters (EPL)
Authors: K. Kosmidis, S. Havlin, A. Bunde
Institutions: Justus-Liebig-Universität Gießen, Bar-Ilan University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2159659875