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, and 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 with the length of edges which in turn has dramatic effects on the topological structure of these networks. We will thoroughly explain 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.
 Publication:

Physics Reports
 Pub Date:
 February 2011
 DOI:
 10.1016/j.physrep.2010.11.002
 arXiv:
 arXiv:1010.0302
 Bibcode:
 2011PhR...499....1B
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Disordered Systems and Neural Networks;
 Computer Science  Social and Information Networks;
 Physics  Physics and Society;
 Quantitative Biology  Neurons and Cognition
 EPrint:
 Review article, revised and augmented version, 86 pages, 86 figures, 338 references