Abstract
Hierarchical social networks appear in a variety of contexts, such as the on-line social network Twitter, the social organization of companies, and terrorist networks. We examine a dynamic model for the disruption of information flow in hierarchical social networks by considering the vertex-pursuit game Seepage played in directed acyclic graphs (DAGs). In Seepage, agents attempt to block the movement of an intruder who moves downward from the source node to a sink. We propose a generalized stochastic model for DAGs with given expected total degree sequence. Seepage is analyzed rigorously in stochastic DAGs in both the cases of a regular and power law degree sequence.
The authors gratefully acknowledge support from Mprime, NSERC, and Ryerson.
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References
Almendral, J.A., López, L., Sanjuán, M.A.F.: Information flow in generalized hierarchical networks. Physica A 324, 424–429 (2003)
Bonato, A.: A Course on the Web Graph. Graduate Studies in Mathematics Series. American Mathematical Society, Providence (2008)
Bonato, A., Nowakowski, R.J.: The Game of Cops and Robbers on Graphs. American Mathematical Society, Providence (2011)
Chayes, J.T., Bollobás, B., Borgs, C., Riordan, O.: Directed scale-free graphs. In: Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms (2003)
Chung, F.R.K., Lu, L.: Complex graphs and networks. American Mathematical Society, Providence (2006)
Clarke, N.E., Finbow, S., Fitzpatrick, S.L., Messinger, M.E., Nowakowski, R.J.: Seepage in directed acyclic graphs. Australasian Journal of Combinatorics 43, 91–102 (2009)
Diestel, R.: Graph theory. Springer, New York (2000)
Farley, J.D.: Breaking Al Qaeda cells: a mathematical analysis of counterterrorism operations (A guide for risk assessment and decision making). Studies in Conflict & Terrorism 26, 399–411 (2003)
Farley, J.D.: Toward a Mathematical Theory of Counterterrorism. The Proteus Monograph Series. Stanford University (2007)
Gupte, M., Muthukrishnan, S., Shankar, P., Iftode, L., Li, J.: Finding hierarchy in directed online social networks. In: Proceedings of WWW 2011 (2011)
Gutfraind, A., Hagberg, A., Pan, F.: Optimal Interdiction of Unreactive Markovian Evaders. In: van Hoeve, W.-J., Hooker, J.N. (eds.) CPAIOR 2009. LNCS, vol. 5547, pp. 102–116. Springer, Heidelberg (2009)
Ikeda, K., Richey, S.E.: Japanese network capital: the impact of social networks on japanese political participation. Political Behavior 27, 239–260 (2005)
López, L., Mendes, J.F.F., Sanjuán, M.A.F.: Hierarchical social networks and information flow. Physica A: Statistical Mechanics and its Applications 316, 695–708 (2002)
Twitaholic, http://twitaholic.com/ (accessed January 10, 2012)
West, D.B.: Introduction to Graph Theory, 2nd edn. Prentice Hall (2001)
Wormald, N.C.: Models of random regular graphs. In: Lamb, J.D., Preece, D.A. (eds.) Surveys in Combinatorics. London Mathematical Society Lecture Note Series, vol. 276, pp. 239–298. Cambridge University Press, Cambridge (1999)
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Bonato, A., Mitsche, D., Prałat, P. (2012). Vertex-Pursuit in Hierarchical Social Networks. In: Agrawal, M., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2012. Lecture Notes in Computer Science, vol 7287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29952-0_11
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