The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Small-World Networks

  • Duncan J. Watts
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_2751

Abstract

The ‘small-world hypothesis’ expresses the idea, long an article of popular belief, that every individual in a given population can reach every other via some ‘short’ chain of intermediaries. Exactly what is ‘short’, how individuals ‘reach’ one other, and how the hypothesis, if true, relates to the structure of social networks are all qsts on which recent progress has been made. Here I describe the genesis of the hypothesis, discuss supporting experimental evidence, and explore some recent mathematical models of small-world networks.

Keywords

Small-world hypothesis Small-world networks 

JEL Classification

D85 
This is a preview of subscription content, log in to check access.

Bibliography

  1. Adamic, L., and E. Adar. 2005. How to search a social network. Social Networks 27: 187–203.CrossRefGoogle Scholar
  2. Adamic, L., R. Lukose, A. Puniyani, and B. Huberman. 2001. Search in power-law networks. Physical Review E 64: 46135–46143.CrossRefGoogle Scholar
  3. Adamic, L., R. Lukose, and B. Huberman. 2003. Local search in unstructured networks. In Handbook of graphs and networks: From the genome to the internet, ed. S. Bornholdt and H. Schuster. Weinheim: Wiley-VCH.Google Scholar
  4. Bernard, H., E. Johnsen, P. Killworth, and S. Robinson. 1991. Estimating the size of an average personal network and of an event population: Some empirical results. Social Science Research 20: 109–121.CrossRefGoogle Scholar
  5. Bollobas, B. 1985. Random graphs. New York: Academic Press.Google Scholar
  6. Chung, F., and L. Lu. 2002. The average distances in random graphs with given expected degrees. Proceedings of the National Academy of Sciences of the United States of America 99: 15879–15882.CrossRefGoogle Scholar
  7. Dodds, P., R. Muhamad, and D. Watts. 2003. An experimental study of search in global social networks. Science 301: 827–829.CrossRefGoogle Scholar
  8. Erdos, P., and A. Renyi. 1959. On random graphs. Publicationes Mathematicae 6: 290–297.Google Scholar
  9. Garfield, E. 1979. It’s a small world after all. In Essays of an information scientist, ed. E. Garfield. Philadelphia: ISI Press.Google Scholar
  10. Guare, J. 1990. Six degrees of separation: A play. New York: Vintage.Google Scholar
  11. Killworth, P., E. Johnsen, R. Bernard, G. Shelley, and C. McCarty. 1990. Estimating the size of personal networks. Social Networks 12: 289–312.CrossRefGoogle Scholar
  12. Kleinberg, J. 2000a. Navigation in a small world. Nature 406: 845.CrossRefGoogle Scholar
  13. Kleinberg, J. 2000b. The small-world phenomenon: An algorithmic perspective. In Proceedings of the 32nd annual ACM symposium on theory of computing. New York: Association of Computing Machinery.Google Scholar
  14. Kleinfeld, J. 2002. The small world problem. Society 39: 61–66.CrossRefGoogle Scholar
  15. Kochen, M. (ed.). 1989. The small world. Norwood: Ablex.Google Scholar
  16. Korte, C., and S. Milgram. 1970. Acquaintance linking between white and negro populations: Application of the small world problem. Journal of Personality and Social Psychology 15: 101–118.CrossRefGoogle Scholar
  17. Liben-Nowell, D., J. Novak, R. Kumar, P. Raghavan, and A. Tomkins. 2005. Geographic routing in social networks. PNAS 102: 11623–11628.CrossRefGoogle Scholar
  18. Milgram, S. 1967. The small world problem. Psychology Today 2: 60–67.Google Scholar
  19. Newman, M. 2000. Models of the small world. Journal of Statistical Physics 101: 819–841.CrossRefGoogle Scholar
  20. Newman, M. 2003. The structure and function of complex networks. Siam Review 45: 167–256.CrossRefGoogle Scholar
  21. Newman, M., A.-L. Barabasi, and D. Watts (eds.). 2006. The structure and dynamics of networks. Princeton: Princeton University Press.Google Scholar
  22. Pool, I., and M. Kochen. 1978. Contacts and influence. Social Networks 1: 1–48.CrossRefGoogle Scholar
  23. Simsek, O., and D. Jensen. 2005. Decentralized search in networks using homophily and degree disparity. In Proceedings of the nineteenth International Joint Conference on Artificial Intelligence (IJCAI 2005). Edinburgh.Google Scholar
  24. Solomonoff, R., and A. Rapoport. 1951. Connectivity of random nets. Bulletin of Mathematical Biophysics 13: 107–117.CrossRefGoogle Scholar
  25. Travers, J., and S. Milgram. 1969. An experimental study of the small world problem. Sociometry 32: 425–443.CrossRefGoogle Scholar
  26. Watts, D. 2004. The ‘new’ science of networks. Annual Review of Sociology 30: 243–270.CrossRefGoogle Scholar
  27. Watts, D., and S. Strogatz. 1998. Collective dynamics of ‘small-world’ networks. Nature 393: 440–442.CrossRefGoogle Scholar
  28. Watts, D., P. Dodds, and M. Newman. 2002. Identity and search in social networks. Science 296: 1302–1305.CrossRefGoogle Scholar
  29. White, H. 1970. Search parameters for small world problem. Social Forces 49: 259–264.CrossRefGoogle Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Duncan J. Watts
    • 1
  1. 1.