[Transitions dans les réseaux spatiaux]
Les réseaux spatiaux peuvent presenter toutes sortes de transitions lorsque leur structure est modifiée. La nature de ces transitions peut différer de l'apparition d'une composante géante, comme c'est le cas pour le graphe d'Erdös–Rényi, et afficher une grande variété de comportements. Nous discuterons ici quelques résultats (la plupart du temps récents) sur les transitions topologiques, les transitions de « localisation » observées dans l'organisation des chemins les plus courts, ainsi que l'effet de la congestion et des fluctuations sur la structure des réseaux optimaux. L'importance des réseaux spatiaux pour les applications pratiques rend ces transitions très pertinentes, et cette revue se veut un pas vers une compréhension plus profonde de l'effet de l'espace sur la structure des réseaux.
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.
Mot clés : Physique statistique, Transitions, Réseaux spatiaux
@article{CRPHYS_2018__19_4_205_0,
author = {Marc Barthelemy},
title = {Transitions in spatial networks},
journal = {Comptes Rendus. Physique},
pages = {205--232},
publisher = {Elsevier},
volume = {19},
number = {4},
year = {2018},
doi = {10.1016/j.crhy.2018.10.006},
language = {en},
}
Marc Barthelemy. Transitions in spatial networks. Comptes Rendus. Physique, Volume 19 (2018) no. 4, pp. 205-232. doi : 10.1016/j.crhy.2018.10.006. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2018.10.006/
[1] Publ. Math. Inst. Hung. Acad. Sci., 5 (1960), p. 17
[2] Publ. Math., 6 (1959), p. 290
[3] Ann. Math. Stat., 30 (1959), p. 1141
[4] J. Soc. Ind. Appl. Math., 9 (1961), p. 533
[5] Random Graphs, Academic Press, London, 1985
[6] Random Geometric Graphs, Oxford Studies in Probability, vol. 5, Oxford University Press, 2003
[7] Percolation, Springer, 1999, pp. 1-31
[8] Introduction to Percolation Theory, CRC Press, 2014
[9] Phys. Rev. B, 31 (1985), p. 4053
[10] Phys. A, 33 (2000), p. L399
[11] J. Phys. A, Math. Gen., 14 (1981), p. L291
[12] Continuum Percolation, vol. 119, Cambridge University Press, 1996
[13] Phys. Rev. E, 93 (2016)
[14] Phys. Rev. E, 67 (2003)
[15] Phys. Rev. E, 66 (2002)
[16] Random Struct. Algorithms, 26 (2005), p. 392
[17] Environ. Plan. A, 9 (1977), p. 185
[18] Nature, 393 (1998), p. 440
[19] Eur. Phys. J. B, 13 (2000), p. 547
[20] Phys. Rev. Lett., 82 (1999), p. 3180
[21] Phys. Rev. Lett., 82 (1999), p. 5180
[22] Phys. Rev. E, 62 (2000), p. 6270
[23] Nature, 406 (2000), p. 845
[24] J. Phys. A, 34 (2001), p. 7749
[25] Phys. Rev. E, 66 (2002)
[26] Phys. Rev. E, 65 (2002)
[27] , 2005 | arXiv
[28] Phys. Rev. E, 73 (2006)
[29] Phys. Rev. E, 60 (1999), p. 7332
[30] Europhys. Lett., 82 (2008)
[31] Phys. Rev. E, 74 (2006)
[32] Biometrika, 42 (1955), p. 425
[33] Nature, 401 (1999), p. 130
[34] Europhys. Lett., 63 (2003), p. 915
[35] Phys. Rev. E, 66 (2002)
[36] Phys. Rev. E, 66 (2002)
[37] Proc. Natl. Acad. Sci. USA, 99 (2002)
[38] , 2018 (preprint) | arXiv
[39] Phys. Rev. E, 68 (2003)
[40] (1971), pp. 283-288
[41] Proceeding of the 29th International Colloquium on Automata, Languages, and Programming (ICALP), Lect. Notes Comput. Sci., vol. 2380, Springer, 2002, pp. 110-122
[42] Evolution and Structure of the Internet: A Statistical Physics Approach, Cambridge University Press, Cambridge, UK, 2003
[43] Proc. Natl. Acad. Sci. USA, 110 (2013) no. 22, pp. 8824-8829
[44] The Gravity Model in Transportation Analysis, VSP, Utrecht, The Netherlands, 1990
[45] Bell Labs Tech. J., 36 (1957), p. 1389
[46] Location Sci., 4 (1996), p. 125
[47] J. Transp. Geogr., 6 (1998), p. 171
[48] Proc. Natl. Acad. Sci. USA, 104 (2007)
[49] Phys. Rev. Lett., 94 (2005)
[50] Phys. Rev. E, 74 (2006)
[51] Europhys. Lett., 50 (2000), p. 1
[52] Phys. Rep., 499 (2011), p. 1
[53] Sociometry, 40 (1977), p. 35
[54] Phys. Rev. E, 64 (2001)
[55] Phys. Rev. Lett., 87 (2001)
[56] Phys. Rev. Lett., 91 (2003)
[57] Eur. Phys. J. B, 38 (2004), p. 163
[58] Phys. Rev. E, 95 (2017)
[59] Nat. Commun., 9 (2018), p. 2501
[60] Int. J. Comput. Inf. Sci., 9 (1980), p. 219
[61] 2015 IEEE International Conference on Communications (ICC), IEEE, 2015, pp. 6450-6455
[62] J. Stat. Mech. (2006)
[63] Morphogenesis of Spatial Networks, Springer, 2018
[64] Algorithmica, 14 (1995), p. 305
[65] Phys. Rev. Lett., 89 (2002)
[66] Traffic Assignment Manuel, US Dept. of Commerce, Urban Planning Division, Washington, DC, 1964
[67] Transp. Res., 10 (1976), p. 223
[68] Phys. Rev. Lett., 84 (2000), p. 4745
[69] Phys. Rev. Lett., 98 (2007)
[70] Phys. Rev. Lett., 104 (2010)
[71] Phys. Rev. Lett., 104 (2010)
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