Abstract.
We study networks that connect points in geographic space, such as transportation networks and the Internet. We find that there are strong signatures in these networks of topography and use patterns, giving the networks shapes that are quite distinct from one another and from non-geographic networks. We offer an explanation of these differences in terms of the costs and benefits of transportation and communication, and give a simple model based on the Monte Carlo optimization of these costs and benefits that reproduces well the qualitative features of the networks studied.
Similar content being viewed by others
References
R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002)
S.N. Dorogovtsev, J.F.F. Mendes, Adv. Phys. 51, 1079 (2002)
M.E.J. Newman, SIAM Rev. 45, 167 (2003)
P. Sen, S. Dasgupta, A. Chatterjee, P.A. Sreeram, G. Mukherjee, S.S. Manna, Phys. Rev. E 67, 036106 (2003)
B.M. Waxman, IEEE J. Selected Areas Comm. 6, 1617 (1988)
S.H. Yook, H. Jeong, A.-L. Barabási, Proc. Natl. Acad. Sci. USA 99, 13382 (2001)
D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998)
J. Brimberg, P. Hansen, K.-W. Lih, N. Mladenovic, M. Breton, Oper. Res. 51, 0228 (2003)
R. Guimerà, S. Mossa, A. Turtschi, L.A.N. Amaral, Proc. Natl. Acad. Sci. USA 102, 7794 (2005)
M.S. Mizruchi, The American Corporate Network, 1904–1974 (Sage, Beverley Hills, 1982)
L.E. Miller, J. Res Natl. Inst. Stand. Technol. 106, 401 (2001)
W.L. Garrison, Papers and Proceedings of the Regional Science Association 6, 121 (1960)
P. Haggett, R.J. Chorley, Network Analysis in Geography (St. Martin's Press, New York, NY, 1969)
K.J. Kansky, Structure of Transportation Networks: Relationships Between Network Geometry and Regional Characteristics (University of Chicago, Chicago, 1963)
S.P. Gorman, R. Kulkarni, Environment and Planning B 31, 273 (2003)
A. Barrat, M. Barthélemy, A. Vespignani, J. Statist. Mech., P05003 (2005)
M. Faloutsos, P. Faloutsos, C. Faloutsos, Comp. Commun. Rev. 29, 251 (1999)
L.A.N. Amaral, A. Scala, M. Barthélémy, H.E. Stanley, Proc. Natl. Acad. Sci. USA 97, 11149 (2000)
M. Molloy, B. Reed, Random Structures and Algorithms 6, 161 (1995)
A.-L. Barabási, R. Albert, Science 286, 509 (1999)
J.M. Kleinberg, Nature 406, 845 (2000)
J. Dall, M. Christensen, Phys. Rev. E 66, 016121 (2002)
S.S. Manna, P. Sen, Phys. Rev. E 66, 066114 (2002)
M. Barthélémy, Europhys. Lett. 63, 915 (2003)
P. Sen, S.S. Manna, Phys. Rev. E 68, 026104 (2003)
T. Petermann, P. de los Rios, preprint cond-mat/0501420 (2005)
M.E.J. Newman, D.J. Watts, Phys. Rev. E 60, 7332 (1999)
D.B. West, Introduction to Graph Theory (Prentice Hall, Upper Saddle River, NJ, 1996)
J.E. Hopcroft, R.E. Tarjan, J. ACM 21, 549 (1974)
G. Csányi, B. Szendrői, Phys. Rev. E 70, 016122 (2004)
A. Fabrikant, E. Koutsoupias, C.H. Papadimitriou, in ICALP (Springer, 2002), Lect. Notes Comput. Sci., Vol. 2380, pp. 110–112
A.J. Scott, Transportation Research 3, 201 (1969)
J. Berg, M. Lässig, Phys. Rev. Lett. 89, 228701 (2002)
R. Xulvi-Brunet, I.M. Sokolov, Phys. Rev. E 66, 026118 (2002)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gastner, M., Newman, M. The spatial structure of networks. Eur. Phys. J. B 49, 247–252 (2006). https://doi.org/10.1140/epjb/e2006-00046-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2006-00046-8