Spatial embedding and the structure of complex networks

Abstract

We review and discuss the structural consequences of embedding a random network within a metric space such that nodes distributed in this space tend to be connected to those nearby. We find that where the spatial distribution of nodes is maximally symmetrical some of the structural properties of the resulting networks are similar to those of random non-spatial networks. However, where the distribution of nodes is inhomogeneous in some way, this ceases to be the case, with consequences for the distribution of neighbourhood sizes within the network, the correlation between the number of neighbours of connected nodes, and the way in which the largest connected component of the network grows as the density of edges is increased. We present an overview of these findings in an attempt to convey the ramifications of spatial embedding to those studying real-world complex systems.

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