A computational model and convergence theorem for rumor dissemination in social networks




The spread of rumors, which are known as unverified statements of uncertain origin, may threaten the society and it's controlling, is important for national security councils of countries. If it would be possible to identify factors affecting spreading a rumor (such as agents’ desires, trust network, etc.) then, this could be used to slow down or stop its spreading. Therefore, a computational model that includes rumor features, and the way rumor is spread among society’s members, based on their desires, is needed. Our research is focused on the relation between the homogeneity of the society and rumor convergence in it. Our result shows that the homogeneity of the society is a necessary condition for convergence of the spread rumor.


[1] Allan J. Kimmel. Rumors and Rumor Control, A manager’s guide to understanding and combatting rumors. Lawarance Erlbaum Assocites Publisher, 1st edition, 2004.

[2] R.H. Knapp. A psychology of rumor. The Public Opinion Quarterly, 8(1):22–37, 1944.

[3] Joseph Nye. Soft Power: The Means To Success In World Politics. Paperback, 2004.

[4] NSA. Cia, propaganda commentary, "our national character". National Security Archive Electronic Briefing Book No. 435, CIA Freedom of Information Act release, 2013.

[5] J. Kostka, Y.A. Oswald, and R Wattenhofer. Word of mouth: Rumor dissemination in social networks. LNCS, 5058:185–196, 2008.

[6] J.R. Piqueira. Rumor propagation model: An equilibrium study. Mathematical Problems in Engineering, pages Article ID 631357, 7 pages, 2010.

[7] D.B. Olles. Rumor Propagation on Random and Small World Networks. Rochester Institute of Technology, 2006.

[8] Z. Zhu and D. Liao. Research of rumors spreading based on transmission dynamics of complex network. In Proceedings of International Conference on Management and Service Science, pages 1–4, 2010.

[9] F. Fu, L. Liu, and L. Wang. Information propagation in hierarchical networks. In Proceedings of 46th IEEE Conference on Decision and Control, page 5329, 2007.

[10] Z. Huang. Self-organized model for information spread in financial markets. The European Physical Journal B, pages 379–385, 2000.

[11] D.J. Daley and D.G. Kendal. Stochastic rumors. Journal of Applied Mathematics, 1:42–55, 1956.

[12] D.J. Daley and J. Gani. Epidemic Modeling. Cambridge University Press, 1st edition, 2000.

[13] B. Pittel. On a daley-kendall model of random rumours. Journal of Applied Probability, 27(1): 14–27, March 1990.

[14] C. Lefevre and P. Picard. Distribution of the final extent of a rumour process. Journal of Applied Probability, 31(1):244–249, 1944.

[15] A. Sudbury. The proportion of the population never hearing a rumour. Journal of Applied Probability, 22(2):443–446, June 1985.

[16] J. Zhou et al. Influence of network structure on rumor propagation. Physic Letters A, 368(6): 458–463, 2007.

[17] H.D. Zanette. Criticality of rumor propagation on small-world networks. NASA Astrophysics Data System, eprint arXiv:condmat 0109049, NASA, 2001.

[18] A.D. Acemoglu, A. Ozdaglar, and A. ParandeGheibi. Spread of (mis)information in social networks. Games and Economic Behavior, 70: 194–227, 2010.

[19] A. Borshchev and A. Filippov. From system dynamics and discrete event to practical agent based modeling: Reasons, techniques, tools. In Proceedings of International Conference of the System Dynamics Society, 2004.

[20] E. Bonabeau. Agent-based modeling: Methods and techniques for simulating human systems. In Proceeding of the National Academy of Science of the United State of America, volume 99, pages 7280–7287, 2002.

[21] L.W. Stern. Zeitschrift fur die gesamte strafechtswissenschaft. Zur Psychologie der Aussage. Experimentelle Untersuchungen uber Erinnerungstreue., XXII, 1902.

[22] Jure Leskovec, Daniel Huttenlocher, and Jon Kleinberg. Predicting positive and negative links in online social networks. In Proceedings of the 19th international conference on World Wide Web, WWW ’10, pages 641–650, New York, NY, USA, 2010. ACM. ISBN 978-1-60558-799-8. doi: 10.1145/1772690.1772756. URL http://doi.acm.org/10.1145/1772690.1772756.

[23] Stephen Guo, Mengqiu Wang, and Jure Leskovec. The role of social networks in online shopping: Information passing, price of trust, and consumer choice. CoRR, abs/1104.0942, 2011.

[24] V.W. Buskens. Social networks and trust, volume 30. Springer, 2002.

[25] MMitchell. An introduction to genetic algorithms. MIT Press, 1st edition, 1998.

[26] P. T. Eugster, R. Guerraoui, A. Kermarrec, and L. Massoulie. From epidemics to distributed computing. IEEE Computer, 37:60–67, 2004.

[27] E. Mollana. Computer simulation in social science. Journal of management and governance, 12 (2):205–211, 2008.

[28] L. Wang, Y. Yue, C. Guo, and X. Zhang. Design of a trust model and finding key-nodes in rumor spreading based on monte-carlo method. In Mobile Adhoc and Sensor Systems, 2009. MASS ’09. IEEE 6th International Conference on, pages 790–795, oct. 2009. doi: 10.1109/MOBHOC.2009.5336916.

[29] M. Nekovee et al. Theory of rumour spreading in complex social networks. Physica A, pages 457–470, 2007.

[30] O.K. Kermack and A.G. McKendrick. Contributions of mathematical theory to epidemics. Royal Society Series A, 141:94–122, 1933.