The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Graph Theory

  • Alan Kirman
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_1232

Abstract

Graphs are used in economics to depict situations in which agents are in direct contact with each other. The use of graph theory enables one to understand the basic properties of the communication network in an economy or market. Typical questions include: how does the structure of a network affect economic outcomes and the welfare of the individuals involved? What happens if agents can choose those with whom they interact? How will networks evolve over time? Theoretical results, economic applications and empirical examples are given.

Keywords

Clusters Coalitions Complete and incomplete information Connectivity Cores First order stochastic domination Graph theory Matching Neighbourhoods Network formation Networks Operations research Power laws Probability Small worlds Spatial economics Spillover effects Stochastic graphs Technological shocks 
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Bibliography

  1. Albert, R., H. Jeong, and A.-L. Barabasi. 2000. Error and attack tolerance of complex networks. Nature 406: 378–382.CrossRefGoogle Scholar
  2. Anderlini, L., and A. Ianni. 1996. Path dependence and learning from neighbours. Games and Economic Behavior 13: 141–177.CrossRefGoogle Scholar
  3. Bollobas, B. 1985. Random graphs. London: Academic Press.Google Scholar
  4. Bramoullé, Y., and R. Kranton. 2007. Public goods in networks. Journal of Economic Theory 135: 478–494.CrossRefGoogle Scholar
  5. Corominas Bosch, M. 2004. Bargaining in a network of buyers and sellers. Journal of Economic Theory 115: 35–77.CrossRefGoogle Scholar
  6. Durlauf, S.N. 1990. Locally interacting systems, coordination failure, and the behavior of aggregate activity. Working paper, Departmetn of Economics, Stanford University.Google Scholar
  7. Durlauf, S.N. 2004. Neighborhood effects. In Handbook of regional and urban economics, ed. J.V. Henderson and J.F. Thisse. Elsevier: North-Holland.Google Scholar
  8. Erdos, P., and A. Renyi. 1960. On the evolution of random graphs. Publications of the Mathematical Institute of the Hungarian Academy of Sciences 5: 17–60.Google Scholar
  9. Evstigneev, I.V., and M. Taksar. 1995. Stochastic equilibria on graphs. Journal of Mathematical Economics 24: 383–406.CrossRefGoogle Scholar
  10. Faloutsos, M., P. Faloutsos, and C. Faloutsos. 1999. On power-law relationships of the internet topology, ACM SIGCOMM ’99. Computers and Communication Review 29: 251–263.CrossRefGoogle Scholar
  11. Frank, H. 1967. Vulnerability of communication networks. IEEE Transactions on Communications 15: 778–779.CrossRefGoogle Scholar
  12. Galeotti, A., S. Goyal, M. Jackson, F. Vega-Redondo, and L. Yariv. 2006. Network games. Mimeo: University of Essex and California Institute of Technology.Google Scholar
  13. Goyal, S. 2006. Learning in games. In Group formation in economics, networks, clubs and coalitions, ed. G. Demange and M. Wooders. Cambridge, UK: Cambridge University Press.Google Scholar
  14. Ioannides, Y.M. 1990. Trading uncertainty and market form. International Economic Review 31: 619–638.CrossRefGoogle Scholar
  15. Ioannides, Y.M. 1997. Evolution of trading structures. In The economy as an evolving complex system II, ed. W.B. Arthur, S.N. Durlauf, and D.A. Lane. Reading: Addison Wesley.Google Scholar
  16. Ioannides, Y.M. 2006. Random graphs and social networks. Discussion Paper No. 518, Department of Economics, Tufts University.Google Scholar
  17. Jackson, M. 2004. A survey of models of network formation: Stability and efficiency. In Group formation in economics; networks, clubs and coalitions, ed. G. Demange and M. Wooders. Cambridge, UK: Cambridge University Press.Google Scholar
  18. Kirman, A. 1983. Communication in markets: A suggested approach. Economics Letters 12: 101–108.CrossRefGoogle Scholar
  19. Kirman, A.P., C. Oddou, and S. Weber. 1986. Stochastic communication and coalition formation. Econometrica 54: 129–138.CrossRefGoogle Scholar
  20. Newman, M., S.H. Strogatz, and D.J. Watts. 2001. Random graphs with arbitrary degree distributions and their applications. Physical Review E 64: 026118.CrossRefGoogle Scholar
  21. Watts, D. 2000. Small worlds. Princeton: Princeton University Press.Google Scholar
  22. Weisbuch, G. 1990. Complex system dynamics. Redwood City: Addison-Wesley.Google Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Alan Kirman
    • 1
  1. 1.