Transitions in spatial networks
arXiv:1810.08764 · doi:10.1016/j.crhy.2018.10.006
Abstract
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.
Corrected version and updated list of references
References in corpus (7)
- Extracting the hierarchical organization of complex systems
- From the betweenness centrality in street networks to structural invariants in random planar graphs
- Structural properties of spatially embedded networks
- Physical realizability of small-world networks
- Interplay between function and structure in complex networks
- Kleinberg Navigation in Fractal Small World Networks
- Topological Phase Transitions in Spatial Networks