SM  Vol.2 No.4 , October 2012
Rumor Spreading and Degree-Related Preference Mechanism on a Small-World Network
ABSTRACT
An alternate model for rumor spreading over small-world networks is suggested, of which two rumors (termed rumor 1 and rumor 2) have different nodes and probabilities of acceptance. The propagation is not symmetric in the sense that when deciding which rumor to adopt, high-degree nodes always consider rumor 1 first, and low-degree nodes always consider rumor 2 first. The model is a natural generalization of the well-known epidemic SIS model and reduces to it when some of the parameters of this model are zero. We find that rumor 1 (preferred by high-degree nodes) is dominant in the network when the degree of nodes is high enough and/or when the network contains large clustered groups of nodes, expelling rumor 2. However, numerical simulations on synthetic networks show that it is possible for rumor 2 to occupy a nonzero fraction of the nodes in many cases as well. Specifically, in the NW small-world model a moderate level of clustering supports its adoption, while increasing randomness reduces it.

Cite this paper
Zhu, Z. , Liu, F. & Liao, D. (2012). Rumor Spreading and Degree-Related Preference Mechanism on a Small-World Network. Sociology Mind, 2, 477-481. doi: 10.4236/sm.2012.24061.
References
[1]   Cane, V. R. (1966). A note on the size of epidemics and the number of people hearing a rumour. J. R. Stat. Soc. Ser. B, 28, 487-490.

[2]   Chakrabarti, D., Wang, Y., Wang, C., Leskovec, J., & Faloutsos, C. (2008). Epidemic thresholds in real networks. ACM Transactions on Information and System Security, 10, 1-26. doi:10.1145/1284680.1284681

[3]   Christley, R. M. et al. (2005). Infection in social networks: Using network analysis to identify high-risk individuals. American Journal of Epidemiology, 162, 1024-1031. doi:10.1093/aje/kwi308

[4]   Daley, D. J., & Kendall, D. G. (1964). Epidemics and rumours. Nature, 204, 1118. doi:10.1038/2041118a0

[5]   Daley, D. J., & Kendall, D. G. (1965). Stochastic rumours. Journal of Applied Mathematics, 1, 42-55. doi:10.1093/imamat/1.1.42

[6]   Draief, M., Ganesh, A., & Massoulie, L. (2008). Thresholds for virus spread on networks. Annals of Applied Probability, 18, 359-378. doi:10.1214/07-AAP470

[7]   Goldenberg, J., Libai, B., Moldovan, S., & Muller, E. (2007). The NPV of bad news. International Journal of Research in Marking, 24, 186-200. doi:10.1016/j.ijresmar.2007.02.003

[8]   Granovetter, M. (1978). Threshold models of collective behavior. American Journal of Sociology, 83, 1420-1443. doi:10.1086/226707

[9]   Guardiola, X., Diaz-Guilera, A., Perez, C. J., Arenas, A., & Llas, M. (2002). Modeling diffusion of innovations in a social network. Physical Review E, 66, Article ID: 026121. doi:10.1103/PhysRevE.66.026121

[10]   Kempe, D., Kleinberg, J., & Tardos, E. (2003). Maximizing the spread of influence in a social network. Proceeding of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 137-146). New York: ACM Press. doi:10.1145/956750.956769

[11]   Landahl, H. D. (1953). On the spread of information with time and distance. Bulletin of Mathematical Biology, 15, 367-381. doi:10.1007/BF02476410

[12]   Liu, Y. H. et al. (2011). Rumor riding: Anonymizing unstructured peer-to-peer systems. IEEE Transactions on Parallel and Distributed Systems, 22, 464-475. doi:10.1109/TPDS.2010.98

[13]   Newman, M. J., Watts, D. J. (1999). Renormalization group analysis of the small-world network model. Physics Letters A, 263, 341-346. doi:10.1016/S0375-9601(99)00757-4

[14]   Rapoport, A., & Rebhun, L. I. (1952). On the mathematical theory of rumor spread. Bulletin of Mathematical Biology, 14, 375-383. doi:10.1007/BF02477853

[15]   Sudbury, A. (1985). The proportion of the population never hearing a rumour. Journal of Applied Probability, 22, 443-446. doi:10.2307/3213787

[16]   Trpevski, D. (2010). Model for rumor spreading over networks. Physical Review E, 81, Article ID: 056102. doi:10.1103/PhysRevE.81.056102

[17]   Watson, R. (1987). On the size of a rumour. Stochastic Processes and Their Applications, 1, 141-149. doi:10.1016/0304-4149(87)90010-X

 
 
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