Spatial Networks

TLDR: In this article, the authors expose the current state of the understanding of how the spatial constraints affect the structure and properties of these networks and review the most recent empirical observations and the most important models of spatial networks.

Abstract: Complex systems are very often organized under the form of networks where nodes and edges are embedded in space Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks, neural networks, are all examples where space is relevant and where topology alone does not contain all the information Characterizing and understanding the structure and the evolution of spatial networks is thus crucial for many different fields ranging from urbanism to epidemiology An important consequence of space on networks is that there is a cost associated to the length of edges which in turn has dramatic effects on the topological structure of these networks We will expose thoroughly the current state of our understanding of how the spatial constraints affect the structure and properties of these networks We will review the most recent empirical observations and the most important models of spatial networks We will also discuss various processes which take place on these spatial networks, such as phase transitions, random walks, synchronization, navigation, resilience, and disease spread