Small and other worlds: Global network structures from local processes

American Journal of Sociology

Volumn 110, Issue 4, 2005, Pages 894-936

  Robins, Garry ^a   Pattison, Philippa ^a   Woolcock, Jodie ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21344457455     PISSN: 00029602     EISSN: None     Source Type: Journal    
DOI: 10.1086/427322     Document Type: Article

References (71)

1. Albert, R., and A.-L. Barabási. 2002. "Statistical Mechanics of Complex Networks." Review of Modern Physics 74:47-97.
2. Amaral, L. A. N., A. Scala, M. Barthélémy, and H. E. Stanley. 2000. "Classes of SmallWorld Networks." Proceedings of the National Academy of Sciences of the United States of America 97:11149-52.
3. Barabási, A. L., and R. Albert. 1999. "Emergence of Scaling in Random Networks." Science 286:509-12.
4. Barrat, A., and M. Weight. 2000. "On the Properties of Small-World Network Models." European Physical Journal B 13:547-60.
5. Barthélémy, M., and L. A. N. Amaral. 1999. "Small-World Networks: Evidence for a Crossover Picture." Physical Review Letters 82:3180-83.
6. Batagelj, V., and A. Mrvar. 2002. Pajek 0.79. Software package. University of Ljubljana.
7. Bearman, P. 1997. "Generalized Exchange." American Journal of Sociology 102: 1383-1415.
8. Besag, J. 1974. "Spatial Interaction and the Statistical Analysis of Lattice Systems." Journal of the Royal Statistical Society B 36:96-127.
9. Bohland, J. W., and A. A. Minai. 2001. "Efficient Associative Memory Using SmallWorld Architecture." N euro computing 38:489-96.
10. Bollobas, B. 1985. Random Graphs. London: Academic Press.
11. Cartwright, D., and F. Harary. 1956. "Structural Balance: A Generalization of Heider's Theory." Psychological Review 63:277-92.
12. Comellas, F., J. Ozon, and J. G. Peters. 2000. "Deterministic Small-World Communication Networks." Information Processing Letters 76:83-90.
13. DeCanio, S. L., C. Dibble, and K. Amir-Atefi. 2000. "The Importance of Organizational Structure for the Adoption of Innovations." Management Science 46:1285-99.
14. Erdös, P., and A. Renyi. 1959. "On Random Graphs. I." Publicationes Mathematicae (Debrecen) 6:290-97.
15. Faust, K., and J. Skvoretz. 2002. "Comparing Networks across Space and Time, Size and Species." Sociological Methodology 32:267-99.
16. Frank, O. 1981. "A Survey of Statistical Methods for Graph Analysis." Pp. 110-55 in Sociological Methodology, edited by S. Leinhardt. San Francisco: Jossey-Bass.
17. Frank, O., and K. Nowicki. 1993. "Exploratory Statistical Analysis of Networks." In Quo Vadis, Graph Theory? edited by J. Gimbel, J. W. Kennedy, and L. V. Quintas. Annals of Discrete Mathematics 55:349-66.
18. Frank, O., and D. Strauss. 1986. "Markov Graphs." Journal of the American Statistical Association 81:832-42.
19. Gilbert, E. N. 1959. "Random Graphs." Annals of Mathematical Statistics 30:1141-44.
20. Gilks, W., S. Richardson, and D. Spiegelhalter. 1996. Markov Chain Monte Carlo in Practice. London: Chapman Hall.
21. Granovetter, M. S. 1973. "The Strength of Weak Ties." American Journal of Sociology 78:1360-80.
22. Grenander, U. 1993. General Pattern Theory. Oxford: Oxford University Press.
23. Handcock, M. S. 2002. "Assessing Degeneracy in Statistical Models for Social Networks." Paper presented at the Workshop on Dynamic Social Network Analysis, Washington, D.C., November.
24. _. 2003. "Statistical Models for Social Networks: Inference and Degeneracy." Pp. 229-40 in Dynamic Social Network Modeling and Analysis, edited by R. Breiger, K. Carley, and P. E. Pattison. Washington, D.C.: National Academies Press.
25. Hoff, P., A. E. Raftery, and M. S. Handcock. 2002. "Latent Space Approaches to Social Network Analysis." Journal of the American Statistical Association 97:1090-98.
26. Holland, P. W., and S. Leinhardt. 1970. "A Method for Detecting Structure in Sociometric Data." American Journal of Sociology 70:492-513.
27. _. 1971. "Transitivity in Structural Models of Small Groups." Comparative Group Studies 2:107-24.
28. Kirillova, O. V. 2001. "Communication Networks with an Emergent Dynamical Structure." Physical Review Letters 87:068701.
29. Kleinberg, J. M. 2000. "Navigation in a Small World." Nature 406:845.
30. Kochen, M. 1989. The Small World. Norwood, N.J.: Ablex.
31. Lazega, E., and P. E. Pattison. 1999. "Social Capital, Multiplex Generalized Exchange and Cooperation in Organizations: A Case Study." Social Networks 21:67-90.
32. Lazega, E., and M. A. J. Van Duijn. 1997. "Position in Formal Structure, Personal Characteristics and Choices of Advisors in a Law Firm: A Logistic Regression Model for Dyadic Network Data." Social Networks 19:375-97.
33. Mathias, N., and V. Gopal. 2001. "Small Worlds: How and Why." Physical Review E 63:021117.
34. Milgram, S. 1967. "The Small World Problem." Psychology Today 2:60-67.
35. Newman, M. E. J. 2000. "Models of the Small-World: A Review." Journal of Statistical Physics 101:819-41.
36. _. 2003. "The Structure and Function of Complex Networks." SI AM Review 45: 167-256.
37. Newman, M. E. J., S. H. Strogatz, and D. J. Watts. 2001. "Random Graphs with Arbitrary Degree Distributions and Their Applications." Physical Review E 64: 026118.
38. Newman, M. E. J., and D. J. Watts. 1999. "Scaling and Percolation in the Small-World Network Model." Physical Review E 60:7332-42.
39. Nowicki, K., and T. A. B. Snijders. 2001. "Estimation and Prediction for Stochastic Blockstructures."Journal of the American Statistical Association 96:1077-87.
40. Padgett, J. F, and C. K. Ansell. 1993. "Robust Action and the Rise of the Medici, 1400-1434." American Journal of Sociology 98:1259-1319.
41. Pandit, S. A., and R. E. Amritkar. 2001. "Random Spread on the Family of SmallWorld Networks." Physical Review E 63:041104.
42. Park, J., and M. E. J. Newman. 2004. "Solution of the 2-Star Model of a Network." Condensed Matter Abstracts 0405457.
43. Pastor-Satorras, R., and A. Vespignani. 2001. "Epidemic Dynamics and Endemic States in Complex Networks." Physical Review E 63:066117.
44. Pattison, P. E. 2002. "Social Networks, Social Space, Social Structure." Keynote address, Sunbelt XXII International Social Network Conference, New Orleans, February.
45. Pattison, P. E., and G. L. Robins. 2002. "Neighborhood Based Models for Social Networks." Sociological Methodology 32:301-37.
46. Pattison, P. E., and S. Wasserman. 1999. "Logit Models and Logistic Regressions for Social Networks, II. Multivariate Relations." British Journal of Mathematical and Statistical Psychology 52:169-94.
47. _. 2002. "Multivariate Random Graph Distributions: Applications to Social Network Analysis." Pp. 74-100 in Festschrift for Ove Frank, edited by J. Hagberg. Stockholm: University of Stockholm, Department of Statistics.
48. Pattison, P. E., S. Wasserman, G. L. Robins, and A. M. Kanfer. 2000. "Statistical Evaluation of Algebraic Constraints for Social Networks." Journal of Mathematical Psychology 44:536-68.
49. Pool, L, and M. Kochen. 1978. "Contacts and Influence." Social Networks 1:1-48.
50. Robins, G. L. 2003. "The Small Worlds of Small Social Networks." Paper presented at the American Association for the Advancement of Science Annual Meeting, Denver, February.
51. Robins, G. L., and M, Alexander. 2004 "Small Worlds in the Social Networks of Interlocking Directorships: Structure and Distance in Bipartite Graphs." Journal of Computational and Mathematical Organization Theory 10:69-94.
52. Robins, G. L., P. Elliott, and P. E. Pattison. 2001. "Network Models for Social Selection Processes." Social Networks 23:1-30.
53. Robins, G. L., and P. E. Pattison. 2001. "Random Graph Models for Temporal Processes in Social Networks." Journal of Mathematical Sociology 25:5-41.
54. _. In press. "Interdependencies and Social Processes: Dependence Graphs and Generalized Dependence Structures." In Models and Methods in Social Network Analysis, edited by P. Carrington, J. Scott, and S. Wasserman. New York: Cambridge University Press.
55. Robins, G. L., P. E. Pattison, and P. Elliott. 2001. "Network Models for Social Influence Processes." Psychometrika 66:161-90.
56. Robins, G. L., P. E. Pattison, and S. Wasserman. 1999. "Logit Models and Logistic Regressions for Social Networks, III. Valued Relations." Psychometrika 64:371-94.
57. Snijders, T. A. B. 1997. "Stochastic Actor-Oriented Models for Network Change." Pp. 185-208 in Evolution of Social Networks, edited by P. Doreian and F. N. Stokman. Amsterdam: Gordon & Breach.
58. _. 2001. "The Statistical Evaluation of Social Network Dynamics." Pp. 361-95 in Sociological Methodology, edited by M. E. Sobel and M. P. Becker. Boston: Basil Blackwell.
59. _. 2002. "Markov Chain Monte Carlo Estimation of Exponential Random Graph Models." Journal of Social Structure 3:2.
60. Snijders, T. A. B., P. E. Pattison, G. L. Robins, and M. S. Handcock. "New Specifications for Exponential Random Graph Models." Manuscript. University of Groninger, Department of Behavioral Sciences.
61. Strauss, D. 1986. "On a General Class of Models for Interaction." SIAM Review 28: 513-27.
62. Strauss, D., and M. Ikeda. 1990. "Pseudolikelihood Estimation for Social Networks." Journal of the American Statistical Association 85:204-12.
63. Strogatz, S. H. 2001. "Exploring Complex Networks." Nature 410:268-76.
64. Van De Bunt, G. G., M. A. J. Van Duijn, and T. A. B. Snijders. 1999. "Friendship Networks through Time: An Actor-Oriented Dynamic Statistical Network Model." Computational and Mathematical Organization Theory 5:167-92.
65. Wasserman, S., and P. E. Pattison. 1996. "Logit Models and Logistic Regressions for Social Networks, I. An Introduction to Markov Random Graphs and p*." Psychometrika 60:401-25.
66. Watts, D. J. 1999a. Small Worlds: The Dynamics of Networks between Order and Randomness. Princeton, N.J.: Princeton University Press.
67. _. 1999b. "Networks, Dynamics, and the Small-World Phenomenon."American Journal of Sociology 105:493-527.
68. Watts, D. J., P. S. Dodds, and M. E. J. Newman. 2002. "Identity and Search in Social Networks." Science 296:1302-5.
69. Watts, D. J., and S. H. Strogatz. 1998. "Collective Dynamics of 'Small World' Networks." Nature 393:440-42.
70. White, H. C., S. A. Boorman, and R. L. Breiger. 1976. "Social Structure from Multiple Networks: I. Blockmodels of Roles and Positions." American Journal of Sociology 87:517-47.
71. Yang, X. S. 2001. "Small-World Networks in Geophysics." Geophysical Research Letters 28:2549-52.