Complexity and Spatial Networks

  • Aura ReggianiEmail author
Living reference work entry


The modern spatial economy has a global “networked” character that is generating important socioeconomic and political changes. In this respect, new forms of connectivity play a significant role through their dynamic and complex interplay with the economic and political driving forces behind globalization. In analyzing such impacts, it is useful to consider the tools and models that have been adopted in regional economics as well as in other disciplines. In this context, it is also necessary to reflect on complexity theory and on the models able to map out the complex interconnected spatial networks.

This chapter begins with a concise review of the most important definitions of complexity, in the light of their relations with spatial networks. There follows an exploration of the main findings from two “close” disciplines, that is, spatial economics and network science, with reference to their associated approaches and modeling tools which are able to grasp complexity from, respectively, the behavioral and the network structure viewpoint. The emerging discussion – with reference to both static and dynamic frameworks through the lens of complexity issues – indicates that (i) a formal correspondence between the fundamental spatial economic models and network models exists and (ii) this correspondence highlights the “simplicity” of the laws underlying complex spatial networks.


Static complexity Dynamic complexity Spatial networks Spatial economic models Network analysis 



The author wishes to thank two referees for their valuable comments.


  1. Adamic LA (2000) Zipf, power-laws, and pareto – a ranking tutorial. Retrieved 4 January 2019 from:
  2. Anas A (1983) Discrete choice theory, information theory and the multinomial logit and gravity models. Transp Res B 17(1):13–23CrossRefGoogle Scholar
  3. Axelrod A, Cohen MD (2000) Harnessing complexity. Basic Books, New YorkGoogle Scholar
  4. Barabási AL, Oltvai ZN (2004) Networks biology: understanding the cell’s functional organization. Nat Rev Genet 5(2):101–113CrossRefGoogle Scholar
  5. Barber MJ, Fischer MM, Scherngell T (2011) The community structure of research and development cooperation in Europe: evidence from a social network perspective. Geogr Anal 43(4):415–432CrossRefGoogle Scholar
  6. Barthélemy M (2010) Spatial networks. Phys Rep 499:1–101. Retrieved 4 January 2019 from: Published in 2011CrossRefGoogle Scholar
  7. Batty M (2005) Cities and complexity: understanding cities with cellular automata, agent-based models, and fractals. MIT Press, Cambridge, MAGoogle Scholar
  8. Batty M (2010) Space, scale, and scaling in entropy-maximising. Geogr Anal 4(1):395–421CrossRefGoogle Scholar
  9. Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang DU (2006) Complex networks: structure and dynamics. Phys Rep 424:175–308CrossRefGoogle Scholar
  10. Caldarelli G, Vespignani A (2007) Large scale structure and dynamics of complex network. World Scientific Publishing, SingaporeCrossRefGoogle Scholar
  11. Casti J (1979) Connectivity, complexity and catastrophe in large scale systems. Wiley, ChichesterGoogle Scholar
  12. Einstein A (1905) Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig? (Does the inertia of a body depend upon its energy-content?). Ann Phys 323(13):639–643. Retrieved 4 January 2019 from: Scholar
  13. Erdös P, Rènyi A (1959) On random graphs. I. Publ Math Debrecen 6:290–297. Retrieved 4 January 2019 from: Scholar
  14. Fischer MM, Leung Y (2001) Geocomputational modelling. Springer, Berlin/Heidelberg/New YorkCrossRefGoogle Scholar
  15. Fotheringham AS, O’Kelly ME (1989) Spatial interaction models. Formulations and applications. Kluwer, DordrechtGoogle Scholar
  16. Gandolfo G (1996) Economic dynamics. Springer, Berlin/Heidelberg/New YorkGoogle Scholar
  17. Heylighen F (1996) What is complexity? Retrieved 4 January 2019 from:
  18. Isard W (1956) Location and space-economy. MIT Press, Cambridge, MAGoogle Scholar
  19. Isard W (1971) On relativity theory and time-space models. Pap Reg Sci Assoc 26:7–24CrossRefGoogle Scholar
  20. Krugman P (1994) Complex landscapes in economic geography. In: Reggiani A, Button K, Nijkamp P (eds) Planning models. Classics in planning. Edward Elgar, Cheltenham, pp 401–405Google Scholar
  21. McFadden D (1974) Conditional logit analysis of qualitative choice behaviour. In: Zarembka P (ed) Frontiers in econometrics. Academic, New York, pp 105–142Google Scholar
  22. Nicolis G, Prigogine I (1977) Self-organisation in non equilibrium systems. Wiley, New YorkGoogle Scholar
  23. Nijkamp P, Reggiani A (1992) Interaction, evolution and chaos in space. Springer, Berlin/Heidelberg/New YorkCrossRefGoogle Scholar
  24. Nijkamp P, Reggiani A (1998) The economics of complex spatial systems. Elsevier, AmsterdamGoogle Scholar
  25. Reggiani A (2004) Evolutionary approaches to transport and spatial systems. In: Hensher DA, Button KJ, Haynes KE, Stopher PR (eds) Handbook of transport geography and spatial systems. Elsevier, Amsterdam, pp 237–252CrossRefGoogle Scholar
  26. Reggiani A (2012) Accessibility, connectivity and resilience in complex networks. In: Geurst KT, Krizek KJ, Reggiani A (eds) Accessibility and transport planning. Edward Elgar, Cheltenham, pp 15–36CrossRefGoogle Scholar
  27. Reggiani A, Nijkamp P (2009) Complexity and spatial networks. Springer, Berlin/Heidelberg/New YorkCrossRefGoogle Scholar
  28. Reggiani A, Nijkamp P (2015) Did Zipf anticipate spatial connectivity structures? Environment and Planning B 42:468–489CrossRefGoogle Scholar
  29. Rose A (2009) Economic resilience to disasters. CARRI Report No. 8, Community and Resilience Institute. Retrieved 4 January 2019 from:
  30. Scott J (2017) Social network analysis, 4th edn. Sage, Newbury ParkGoogle Scholar
  31. Sen A, Smith TE (1995) Gravity models of spatial interaction behavior. Springer, Berlin/Heidelberg/New YorkCrossRefGoogle Scholar
  32. Simon H (1962) The architecture of complexity. Proc Am Philos Soc 106(6):467–482Google Scholar
  33. Tsiotas D, Polyzos S (2018) The complexity in the study of spatial networks: an epistemological approach. Netw Spat Econ 18(1):1–32CrossRefGoogle Scholar
  34. Weaver W (1948) Science and complexity. Am Sci 36:536–544Google Scholar
  35. Wilson A (1970) Entropy in urban and regional modelling. Pion, LondonGoogle Scholar
  36. Zipf GK (1949) Human behaviour and the principle of least effort. Addison-Wesley Press, Cambridge, MAGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of BolognaBolognaItaly

Personalised recommendations