Delay of Social Search on Small-World Graphs

Journal of Mathematical Sociology

Volumn 38, Issue 1, 2014, Pages 1-46

  Inaltekin, Hazer ^a   Chiang, Mung ^b   Poor, H Vincent ^b  

^a ANTALYA INTERNATIONAL UNIVERSITY   (Turkey)

^b Princeton University   (United States)

Author keywords

delay of social search; scale free networks; small world networks; small world phenomenon; social networks; social search

Indexed keywords

EID: 84890948965     PISSN: 0022250X     EISSN: 15455882     Source Type: Journal    
DOI: 10.1080/0022250X.2011.629062     Document Type: Article

References (81)

1. Adamic, L. A., Lukose, R. M., Puniyani A. R., & Huberman, B. A. (2001). Search in power-law networks. Physical Review E, 64, Article 046135.
2. Amaral, L. A. N., Scala, A., Barthelemy, M., Stanley, H. E. (2000). Classes of small-world networks. Proceedings of the National Academy of Sciences, 97, 11149 - 11152.
3. Axelrod, R. (1997). The dissemination of culture: a model with local convergence and global polarization. The Journal of Conflict Resolution, 41, 203 - 226.
4. Axtell, R. L., Epstein, J. M., Dean, J. S., Gumerman, G. J., Swedlund, A. C., Harburger, J., Parker, M. (2002). Population growth and collapse in a multiagent model of the Kayenta Anasazi in Long House Valley. Proceedings of the National Academy of Sciences, 99, 7275 - 7279.
5. Barabási, A.-L. (2002). Linked: The new science of networks. Cambridge, MA: Perseus.
6. Barnett, G. A. (1989). Approaches to non-Euclidean network analysis. In M. Kochen (Ed.), The small world (pp. 349 - 372). Norwood, NJ: Ablex.
7. Bassett, D. S., & Bullmore, E. (2006). Small-world brain networks. Neuroscientist, 12, 512 - 523.
8. Bearman, P. S., Moody, J., & Stovel, K. (2004). Chains of affection: The structure of adolescent romantic and social networks. American Journal of Sociology, 110, 44 - 91.
9. Bell, D. C., Belli-McQueen, B., & Haider, A. (2007). Partner naming and forgetting: Recall of network members. Social Networks, 29, 279 - 299.
10. Bernard, H. R., Johnsen, E. C., Killworth, P. D., & Robinson, S. (1991). Estimating the size of an average personal network and of an event population: Some empirical results. Social Science Research, 20, 109 - 121.
11. Bernard, H. R., Killworth, P. D., Johnsen, E. C., Shelley, G. A., & McCarty, C. (2001). Estimating the ripple effect of a disaster. Connections, 24, 18 - 22.
12. Bollobás, B. (2001). Random graphs. Cambridge, UK: Cambridge University Press.
13. Burt, R. S. (1992). Structural holes: The social structure of competition. Cambridge, MA: Harvard University Press.
14. Callaway, D. S., Newman, M. E. J., Strogatz, S. H., & Watts, D. J. (2000). Network robustness and fragility: Percolation on random graphs. Physical Review Letters, 85, 5468 - 5471.
15. Centola, D., & Macy, M. (2007). Complex contagions and the weakness of long ties. American Journal of Sociology, 113, 702 - 734.
16. Centola, D., Willer, R., & Macy, M. (2005). The emperor's dilemma: A computational model of self-enforcing norms. American Journal of Sociology, 110, 1009 - 1040.
17. Chaintreau, A., Fraigniaud, P., & Lebhar, E. (2008). Networks become navigable as nodes move and forget. In Proceedings of the 35th International Colloquium on Automata, Languages and Programming (pp.133-144). Berlin, Germany: Springer-Verlag.
18. Clauset, A., & Moore, C. (2003). How do networks become navigable? Retrieved from http://arxiv.org/abs/cond-mat/0309415
19. Cohen, J. E., Briand, F., & Newman, C. M. (1990). Community food webs: Data and theory. Berlin, Germany: Springer.
20. Cohen, L., Frazzini, A., & Malloy, C. (2008). The small world of investing: Board connections and mutual fund returns. Journal of Political Economy, 116, 951 - 979.
21. Coleman, J., Katz, E., & Menzel, H. (1957). The diffusion of an innovation among physicians. Sociometry, 20, 253 - 270.
22. Davidson, M. L. (1983). Multidimensional scaling. New York, NY: Wiley.
23. Dodds, P. S., Muhamad, R., & Watts, D. J. (2003). An experimental study of search in global social networks. Science, 301, 827 - 829.
24. Donovan, P. (2007). How idle is idle talk? One hundred years of rumor research. Diogenes, 54, 59 - 83.
25. Duchon, P., Hanusse, N., Lebhar, E., & Schabanel, N. (2006). Could any graph be turned into a small-world? Theoretical Computer Science, 355, 96 - 103.
26. Dunbar, R. I. M. (1993). Coevolution of neocortical size, group size and language in humans. Behavioral and Brain Sciences, 16, 681 - 735.
27. Epstein, J. M. (1999). Agent-based computational models and generative social science. Complexity, 4, 41 - 60.
28. Erickson, B. H., & Kringas, P. (1975). Small world of politics, or seeking elites from bottom up. Canadian Research Sociology Quarterly, 12, 585 - 593.
29. Fraigniaud, P., & Giakkoupis, G. (2009). The effect of power-law degrees on the navigability of small worlds. In Proceedings of the 28th ACM Symposium on Principles of Distributed Computing (pp. 240-249). New York, NY: ACM.
30. Franceschetti, M., & Meester, R. (2006). Navigation in small-world networks: A scale-free continuum model. Journal of Applied Probability, 43, 1173 - 1180.
31. Goel, S., Muhamad, R., & Watts, D. J. (2009). Social search in "small-world" experiments. In Proceedings of the 18th International World Wide Web Conference (pp. 701-710). New York, NY: ACM.
32. Gowaikar, R., & Hassibi, B. (2006). Communication over a wireless network with random connections. IEEE Transactions on Information Theory, 52, 2857 - 2871.
33. Granovetter, M. S. (1973). The strength of weak ties. American Journal of Sociology, 78, 1360 - 1380.
34. Granovetter, M. S. (1983). The strength of weak ties: A network theory revisited. Sociological Theory, 1, 201 - 233.
35. Guiot, J. M. (1976). A modification of Milgram's small world method. European Journal of Social Psychology, 6, 503 - 507.
36. Gupta, P., & Kumar, P. R. (2000). The capacity of wireless networks. IEEE Transactions on Information Theory, 46, 388 - 404.
37. Hekmat, R., & Mieghem, P. V. (2004). Study of connectivity in wireless ad hoc networks with an improved radio model. In Proceedings of the 2nd Workshop on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (pp. 142-151). New York, NY: IEEE.
38. Hill, R. A., & Dunbar, R. I. M. (2003). Social network size in humans. Human Nature, 14, 53 - 72.
39. Inaltekin, H., Chiang, M., & Poor, H. V. (2010). Average message delivery time for small-world networks in the continuum limit. IEEE Transactions on Information Theory, 56, 4447 - 4470.
40. Killworth, P. D., McCarty, C., Bernard, H. R., & House, M. (2006). Social networks: the accuracy of small world chains in sociological networks. Social Networks, 28, 85 - 96.
41. Kleinberg, J. M. (2000a). Navigation in a small world. Nature, 406, 845.
42. Kleinberg, J. M. (2000b). The small-world phenomenon: An algorithmic perspective. In Proceedings of the 32nd ACM Symposium on Theory of Computing (pp. 163 - 170). New York, NY: ACM.
43. Kleinfeld, J. (2002). The small world problem. Society, 39, 61 - 66.
44. Klovdahl, A. S. (1985). Social networks and the spread of infectious diseases: The AIDS example. Social Science and Medicine, 21, 1203 - 1216.
45. Kochen, M. (1985). The structure of acquaintance nets and rates of social development. Social Networks, 7, 323 - 339.
46. Korte, C., & Milgram, S. (1970). Acquaintance linking between white and Negro populations: applications of the small world problem. Journal of Personality and Social Psychology, 15, 101 - 118.
47. Kossinets, G., & Watts, D. J. (2006). Empirical analysis of an evolving social network. Science, 311, 88 - 90.
48. Lee, N. H. (1969). The search for an abortionist. Chicago, IL: University of Chicago Press.
49. Leskovec, J., & Horvitz, E. (2008). Planetary-scale views on a large instant-messaging network. In Proceedings of the 17th International World Wide Web Conference (pp. 915 - 924). New York, NY: ACM.
50. Lin, N., Dayton, P. W., & Greenwald, P. (1977). The urban communication network and social stratification: A "small world" experiment. In B. D. Ruben (Ed.), Communication yearbook (pp. 107 - 119). New Brunswick, NJ: Transaction Book.
51. Macy, M. W., & Willer, R. (2002). From factors to actors: computational sociology and agent-based modeling. Annual Review of Sociology, 28, 143 - 166.
52. Malaquias, J. L., Rosa, A. C., & Correia, C. M. B. A. (2006). A small-world model of the human mind. In Proceedings of the 2006 ACM Symposium on Applied Computing (pp. 15-22) New York, NY: ACM.
53. Manku, G. S., Bawa, M., & Raghavan, P. (2003). Symphony: Distributed hashing in a small world. In Proceedings of the 4th USENIX Symposium on Internet Technologies and Systems (pp. 127-140). Berkeley, CA: USENIX
54. McCarty, C., Killworth, P. D., Bernard, H. R., Johnsen, E., & Shelley, G. A. (2001). Comparing two methods for estimating network size. Human Organization, 60, 28 - 39.
55. Milgram, S. (1967). The small world problem. Psychology Today, 1, 61 - 67.
56. Moody, J. (2002). The importance of relationship timing for diffusion. Social Forces, 81, 25 - 56.
57. Newman, M. E. J. (2001). The structure of scientific collaboration networks. Proceedings of the National Academia of Sciences, 98, 404 - 409.
58. Newman, M. E. J. (2003a). Ego-centered networks and the ripple effect. Social Networks, 25, 83 - 95.
59. Newman, M. E. J. (2003b). The structure and function of complex networks. SIAM Review, 45, 167 - 256.
60. Newman, M. E. J., Moore, C., & Watts, D. J. (2000). Mean-field solution of the small-world network model. Physical Review Letters, 84, 3201 - 3204.
61. Nguyen, V., & Martel, C. U. (2006). Designing low cost networks with short routes and low congestion. In Proceedings of the 25th IEEE International Conference on Computer Communications (pp. 1-12). New York, NY: IEEE.
62. Nowak, M. A., & Sigmund, K. (1992). Tit for tat in heterogenous populations. Nature, 355, 250 - 253.
63. Nowell, D. L., Novak, J., Kumar, R., Raghavan, P., & Tomkins, A. (2005). Geographic routing in social networks. Proceedings of the National Academy of Sciences, 102, 11623 - 11628.
64. Penrose, M. (2003). Random geometric graphs. New York, NY: Oxford University Press.
65. Pool, I. D. S., & Kochen, M. (1978). Contacts and influence. Social Networks, 1, 5 - 51.
66. Rapoport, A. (1963). Mathematical models of social interaction. In R. D. Luce, R. R. Bush, & E. Galanter, (Eds.), Handbook of mathematical psychology (pp. 493 - 579). New York, NY: John Wiley and Sons.
67. Rudin, W. (1987). Real and complex analysis. New York, NY: McGraw-Hill.
68. Schelling, T. C. (1971). Dynamic models of segregation. Journal of Mathematical Sociology, 1, 143 - 186.
69. Schenettler, S. (2009a). A small world on feet of clay? A comparison of empirical small-world studies against best-practice criteria. Social Networks, 31, 179 - 189.
70. Schenettler, S. (2009b). A structured overview of 50 years of small-world research. Social Networks, 31, 165 - 178.
71. Shotland, R. L. (1976). University communication networks: The small world method. New York, NY: Wiley.
72. Stevenson, W. B., Davidson, B., Manev, I., & Walsh, K. (1997). The small world of the university: a classroom exercise in the study of networks. Connections, 20, 23 - 33.
73. Strogatz, S. H. (2001). Exploring complex networks. Nature, 410, 268 - 276.
74. Travers, J., & Milgram, S. (1969). An experimental study of the small world problem. Sociometry, 32, 425 - 443.
75. Watts, D. J. (1999). Small worlds: The dynamics of networks between order and randomness. Princeton, NJ: Princeton University Press.
76. Watts, D. J. (2003). Six degrees: The science of a connected age. New York, NY: Norton & Company.
77. Watts, D. J. (2004). The "new" science of networks. Annual Review of Sociology, 30, 243 - 270.
78. Watts, D. J., Dodds, P. S., & Newman, M. E. J. (2002). Identity and search in social networks. Science, 296, 1302 - 1304.
79. Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of small-world networks. Nature, 393, 440 - 442.
80. Weimann, G. (1983). The not-so-small world-Ethnicity and acquaintance networks in Israel. Social Networks, 5, 289 - 302.
81. Williams, R. J., & Martinez, N. D. (2000). Simple rules yield complex food webs. Nature, 404, 180 - 183.