Spatial Networks

TL;DR

Spatial networks, where nodes and edges are embedded in space, are crucial for understanding various real-world systems, and spatial constraints significantly influence their structure and dynamics.

Contribution

This paper thoroughly reviews current understanding, empirical observations, models, and processes related to spatial networks, highlighting the impact of spatial constraints.

Findings

Spatial constraints affect network topology and properties.

Recent models capture the influence of space on network structure.

Processes like disease spread and synchronization are shaped by spatial embedding.

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.