2018/05/01 by Marc Barthélemy, Marc Barthelemy
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Complex Network Analysis Techniques #Computer science #Humanities #Mathematics #Network structure #Opinion Dynamics and Social Influence #Opportunistic and Delay-Tolerant Networks #Philosophy #Theoretical computer science #Topology (electrical circuits) #cond-mat.dis-nn #cond-mat.stat-mech #physics.soc-ph
paper · pdf · doi:10.1016/j.crhy.2018.10.006
published as Comptes Rendus Physique 19(4), 205-232 (2018) · Corrected version and updated list of references
openalex publication_date 2018/05/01 · arxiv created 2018/12/18 · arxiv updated 2018/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 Erdös–Rényi 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.