Networks and Spatial Economics

, Volume 7, Issue 4, pp 301–313 | Cite as

Using Raster-Based GIS and Graph Theory to Analyze Complex Networks

  • Laurie A. Schintler
  • Rajendra Kulkarni
  • Sean Gorman
  • Roger Stough


Disruptions to transportation networks can be very costly. However, managing disruptions and the costs associated with these events, poses some challenges. Transport networks are, in many cases, large and complex. This paper develops a method, based on complex network theory, to analyse transportation networks. It provides a way, through the use raster-based geographic information system (GIS) techniques, to identify critical nodes or links in a network that reflect spatial interdependencies with other networks and to assess how resilient the networks are to failures of these locations. For purposes of illustration, the method is applied to the network of major roads and rail in the State of Florida.


Complex networks Geographic information system (GIS) Raster analysis Transportation Spatial interdependencies 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Albert R, Barabási A (2002) Statistical mechanics of complex networks. Rev Mod Phys 74:47–97CrossRefGoogle Scholar
  2. Albert R, Jeong H, Barabási A-L (2000) Attack and error tolerance in complex networks. Nature 406(6794):378–382CrossRefGoogle Scholar
  3. Alderson D, Doyle J, Govindan R, Willinger W (2003). Toward an optimization-driven framework for designing and generating realistic Internet topologies. ACM SIGCOMM Comput Commun Rev 33:41–46CrossRefGoogle Scholar
  4. Amaral L, Scala A, Barthelemy M, Stanley HE (2000) Classes of small-world networks. Proc Natl Acad Sci USA 97:11149–11152CrossRefGoogle Scholar
  5. Barabasi A (2001a) The physics of the web physics world. Physics World, July 2001Google Scholar
  6. Barabasi A (2001b) The physics of the web. Physics World 97:11149–11152Google Scholar
  7. Barabasi A, Albert A (1999) Emergence of scaling in random networks. Science 286:509–512CrossRefGoogle Scholar
  8. Barthelemy M (2003) Crossover from scale-free to spatial networks. Europhys Lett 63:915–921CrossRefGoogle Scholar
  9. Callaway DS, Newman MEJ, Strogatz SH, Watts DJ (2000) Network robustness and fragility: percolation on random graphs. Phys Rev Lett 85:5468–5471CrossRefGoogle Scholar
  10. Chen Q, Hyunseok C, Govindan R, Sugih J, Schenker S, Willinger W (2001) The origin of power laws in Internet topologies revisited. Proceedings of IEEE Infocom 2002(2):608–617Google Scholar
  11. Cohen R, Erez K, Ben-Avraham D, Havlin S (2001) Breakdown of the Internet under intentional attack. Phys Rev Lett 86:3682–3685CrossRefGoogle Scholar
  12. Erdos P, Rényi A (1960) On the evolution of random graphs. Publ Math Inst Hungar Acad Sci 5:17–61Google Scholar
  13. Faloutsos M, Faloutsos C, Faloutsos P (1999) On power–law relationships of the Internet topology. Comput Commun Rev 29:251–262CrossRefGoogle Scholar
  14. Garrison W (1960) Connectivity of the interstate highway system. Pap Proc Reg Sci Assoc 6:121–137CrossRefGoogle Scholar
  15. Gorman SP, Kulkarni R (2004) Spatial small worlds: new geographic patterns for an information economy. Environ Plan B 31:273–296CrossRefGoogle Scholar
  16. Gorman SP, Malecki EJ (2000) The networks of the Internet: an analysis of provider networks. Telecommun Policy 24:113–134CrossRefGoogle Scholar
  17. Gorman SP, Schintler L, Kulkarni R, Stough R (2004) The revenge of distance: vulnerability analysis of critical infrastructure. J Conting Crisis Manag 12:48–63CrossRefGoogle Scholar
  18. Grubesic TH, O’Kelly ME, Murray AT (2003) A geographic perspective on telecommunication network survivability. Telemat Inform 20:51–69CrossRefGoogle Scholar
  19. Haggett P, Chorley R (1969) Network analysis in geography. New York, NY, USA: St. Martins PressGoogle Scholar
  20. Jain AK, Murty MN, Flynn PJ (1999) Data clustering: review. ACM Comput Surv 31:264–323CrossRefGoogle Scholar
  21. Kansky K (1963) Structure of transportation networks: relationships between network geometry and regional characteristics. University of Chicago, Department of Geography, Research PapersGoogle Scholar
  22. Lakhina A, Byers JW, Crovella M, Matta I (2002) On the geographic locations of Internet resources
  23. Malecki EJ (2002) The economic geography of the Internet’s infrastructure. Econ Geogr 78:399–424Google Scholar
  24. Nyusten JD, Dacey MF (1968) A graph theory interpretation of nodal regions. In: Berry B, Marble D (eds) Spatial analysis. Prentice Hall, Englewood Cliffs, pp 407–418Google Scholar
  25. O’Kelly ME, Grubesic TH (2002) Backbone topology, access, and the commercial Internet, 1997–2000. Environ Plan B 29:533–552CrossRefGoogle Scholar
  26. Reed WR (1970) Indirect connectivity and hierarchies of urban dominance. Ann Assoc Am Geogr 60:770–785CrossRefGoogle Scholar
  27. Roth J (1955) An application of algebraic topology to numerical analysis: on the existence of a solution to the network problem. Proc Natl Acad Sci 41:518–521CrossRefGoogle Scholar
  28. Schintler L, Gorman S, Reggiani A, Patuelli R, Gillespie A, Nijkamp P, Rutherford J (2005) Complex network phenomena in telecommunications systems. Netw Spatial Econ 5:351–370CrossRefGoogle Scholar
  29. Schintler L, Kulkarni R, Gorman S, Stough R (2006) Power and packets: a spatial network comparison of the U.S. electric power grid and the Internet network. In: Reggiani A, Nijkamp P (eds) Spatial dynamics, networks and modelling. Edward Elgar, Cheltenham and Northampton, pp 35–60Google Scholar
  30. Taffee EJ, Gauthier HL (1973) Geography of transportation. Prentice Hall, Englewood CliffsGoogle Scholar
  31. Taubin G (1995) A signal processing approach to fair surface design. In: R Cook (ed) Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques, pp 351–358Google Scholar
  32. Townsend A (2001) Network cities and the global structure of the Internet. Am Behav Sci 44:1697–1716CrossRefGoogle Scholar
  33. Wallace R, Ong P, Schwartz E (1994) Space variant image processing. Int J Comput Vis 13:71–90CrossRefGoogle Scholar
  34. Wandell B, Chias S, Backus BT (2000) Visualization and measurement of the cortical surface. J Cogn Neurosci 12:739–752CrossRefGoogle Scholar
  35. Watts DJ, Strogatz SH (1998) Collective dynamics of small-world networks. Nature 363:202–204Google Scholar
  36. Wheeler DC, O’Kelly ME (1999) Network topology and city accessibility of the commercial Internet. Prof Geogr 51:327–339CrossRefGoogle Scholar
  37. Yook SH, Jeong H, Barabási AL (2001) Modeling the Internet’s large-scale topology
  38. Zahn C (1971) Graph theoretical methods for detecting and describing gestalt clusters. IEEE Trans Comput 20:68–86CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Laurie A. Schintler
    • 1
  • Rajendra Kulkarni
    • 1
  • Sean Gorman
    • 1
  • Roger Stough
    • 1
  1. 1.School of Public PolicyGeorge Mason UniversityFairfaxUSA

Personalised recommendations