Marc Barthelemy
Published 2018-10-20Version 1
Networks embedded in space can display all sorts of transitions when their structure is modified. The nature of these transitions (and in some cases crossovers) can differ from the usual appearance of a giant component as observed for the Erdos-Renyi graph, and spatial networks display a large variety of behaviors. We will discuss here some (mostly recent) results about topological transitions, `localization' transitions seen in the shortest paths pattern, and also about the effect of congestion and fluctuations on the structure of optimal networks. The importance of spatial networks in real-world applications makes these transitions very relevant and this review is meant as a step towards a deeper understanding of the effect of space on network structures.
Comments: To appear in the special issue "Spatial Networks" in the Comptes Rendus Physique
Thermodynamics and Legendre Duality in Optimal Networks
Fundamental physical constants set the observability and operation of phase and other transitions and increase entropy
Majorization requires infinitely many second laws
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