Encyclopedia of Social Network Analysis and Mining

Living Edition
| Editors: Reda Alhajj, Jon Rokne

Spatial Networks

Living reference work entry
DOI: https://doi.org/10.1007/978-1-4614-7163-9_40-1

Synonyms

Glossary

Graph

(or Network) A set of vertices connected by edges

Adjacency Matrix

A matrix A which represents the structure of a graph. The element Aij is either 0 if i and j are not connected or Aij = 1 if there is an edge from i to j. For a spatial network, the position of the nodes {xi} is needed in order to completely characterize the network

Betweenness Centrality

The betweenness centrality of a vertex (or an edge) x is defined as \( BC(x)={\sum}_{s, t\in V}\frac{\sigma_{s t}(x)}{\sigma_{s t}} \)

Keywords

Transportation 
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References

  1. Albert R, Barabasi AL (2002) Statistical mechanics of complex networks. Rev Mod Phys 74:47MathSciNetCrossRefMATHGoogle Scholar
  2. Aldous DJ, Shun J (2010) Connected spatial networks over random points and a route-length statistic. Stat Sci 25:275–288MathSciNetCrossRefMATHGoogle Scholar
  3. Barrat A, Barthelemy M, Pastor-Satorras R, Vespignani A (2004) The architecture of complex weighted networks. Proc Natl Acad Sci USA 101:3747CrossRefGoogle Scholar
  4. Barthelemy M (2011) Spatial networks. Phys Rep 499:1MathSciNetCrossRefGoogle Scholar
  5. Barthelemy M, Flammini A (2008) Modelling urban street patterns. Phys Rev Lett 100:138702CrossRefGoogle Scholar
  6. Barthelemy M, Bordin P, Berestycki H, Gribaudi M (2013) Self-organization versus top-down planning in the evolution of a city. Nat Sci Rep 3:2153Google Scholar
  7. Batty M (2005) Network geography: relations, interactions, scaling and spatial processes in GIS. In: Fisher PF, Unwin DJ (eds) Re-presenting GIS. Wiley, Chich-ester, pp 149–170Google Scholar
  8. Buhl J, Gautrais J, Reeves N, Solé RV, Valverde S, Kuntz P, Theraulaz G (2006) Topological patterns in street networks of self-organized urban settlements. Eur Phys J B-Condens Matter Complex Syst 49(4):513–522CrossRefGoogle Scholar
  9. Bullmore E, Sporns O (2009) Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Rev Neurosci 10(3):186–198CrossRefGoogle Scholar
  10. Clark J, Holton DA (1991) A first look at graph theory, vol 6. World Scientific, TeaneckCrossRefMATHGoogle Scholar
  11. Crucitti P, Latora V, Porta S (2006) Centrality in networks of urban streets. Chaos Interdiscip J Nonlinear Sci 16(1):015113–015113CrossRefMATHGoogle Scholar
  12. Freeman LC (1977) A set of measures of centrality based on betweenness. Sociometry 40:35–41CrossRefGoogle Scholar
  13. Fujita M, Krugman PR, Venables AJ (1999) The spatial economy: cities, regions and international trade, vol 213. MIT, CambridgeMATHGoogle Scholar
  14. Haggett P, Chorley RJ (1969) Network analysis in geography. Edward Arnold, LondonGoogle Scholar
  15. Kissling CC (1969) Linkage importance in a regional highway network. Can Geogr 13:113–129CrossRefGoogle Scholar
  16. Lammer S, Gehlsen B, Helbing D (2006) Scaling laws in the spatial structure of urban road networks. Phys A Stat Mech Appl 363(1):89–95CrossRefGoogle Scholar
  17. Latora V, Marchiori M (2001) Efficient behavior of small-world networks. Phys Rev Lett 87:198701CrossRefGoogle Scholar
  18. Liben-Nowell D, Novak J, Kumar R, Raghavan P, Tomkins A (2005) Geographic routing in social networks. Proc Natl Acad Sci USA 102:11623–11628CrossRefGoogle Scholar
  19. Radke JD (1977) Stochastic models in circuit network growth. Thesis and dissertations (Comprehensive). Paper 1450, Wilfrid Laurier UniversityGoogle Scholar
  20. Strano E, Nicosia V, Latora V, Porta S, Barthelemy M (2012) Elementary processes governing the evolution of road networks. Nat Sci Rep 2:296Google Scholar
  21. Tero A, Takagi S, Saigusa T, Ito K, Bebber DP, Fricker MD, Yumiki K, Kobayashi R, Nakagaki T (2010) Rules for biologically inspired adaptive network design. Sci Signal 327:439MathSciNetMATHGoogle Scholar
  22. Watts D, Strogatz S (1998) Collective dynamics of small-world networks. Nature 393:440–442CrossRefGoogle Scholar
  23. Xie F, Levinson D (2007) Measuring the structure of road networks. Geogr Anal 39:336–356CrossRefGoogle Scholar
  24. Xie F, Levinson D (2009) Topological evolution of surface transportation networks. Comput Environ Urban Syst 33:211–223CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media LLC 2017

Authors and Affiliations

  1. 1.Institut de Physique ThéoriqueCEAGif-sur-YvetteFrance