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Burning a Graph as a Model of Social Contagion

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Algorithms and Models for the Web Graph (WAW 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8882))

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Abstract

We introduce a new graph parameter called the burning number, inspired by contact processes on graphs such as graph bootstrap percolation, and graph searching paradigms such as Firefighter. The burning number measures the speed of the spread of contagion in a graph; the lower the burning number, the faster the contagion spreads. We provide a number of properties of the burning number, including characterizations and bounds. The burning number is computed for several graph classes, and is derived for the graphs generated by the Iterated Local Transitivity model for social networks.

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References

  1. Alon, N., Prałat, P., Wormald, N.: Cleaning regular graphs with brushes. SIAM Journal on Discrete Mathematics 23, 233–250 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  2. Balogh, J., Bollobás, B., Morris, R.: Graph bootstrap percolation (preprint 2014)

    Google Scholar 

  3. Banerjee, S., Das, A., Gopalan, A., Shakkottai, S.: Epidemic spreading with external agents. In: Proceedings of IEEE Infocom (2011)

    Google Scholar 

  4. Barghi, A., Winkler, P.: Firefighting on a random geometric graph. Random Structures and Algorithms (accepted)

    Google Scholar 

  5. Bonato, A., Hadi, N., Horn, P., Prałat, P., Wang, C.: Models of on-line social networks. Internet Mathematics 6, 285–313 (2011)

    Article  Google Scholar 

  6. Bonato, A., Janssen, J., Roshanbin, E.: Burning a graph is hard (preprint 2014)U

    Google Scholar 

  7. Bonato, A., Nowakowski, R.J.: The Game of Cops and Robbers on Graphs. American Mathematical Society, Providence (2011)

    MATH  Google Scholar 

  8. Domingos, P., Richardson, M.: Mining the network value of customers. In: Proceedings of the 7th International Conference on Knowledge Discovery and Data Mining (KDD) (2001)

    Google Scholar 

  9. Finbow, S., King, A., MacGillivray, G., Rizzi, R.: The firefighter problem for graphs of maximum degree three. Discrete Mathematics 307, 2094–2105 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  10. Finbow, S., MacGillivray, G.: The Firefighter problem: a survey of results, directions and questions. Australasian Journal of Combinatorics 43, 57–77 (2009)

    MATH  MathSciNet  Google Scholar 

  11. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, W.H (1979)

    Google Scholar 

  12. Haynes, T.W., Hedetniemi, S.T., Slater, P.J.: Fundamentals of Domination in Graphs. Marcel Dekker, New York (1998)

    MATH  Google Scholar 

  13. Kempe, D., Kleinberg, J., Tardos, E.: Maximizing the spread of influence through a social network. In: Proceedings of the 9th International Conference on Knowledge scovery and Data Mining (KDD) (2003)

    Google Scholar 

  14. Kempe, David, Kleinberg, Jon M., Tardos, Éva: Influential Nodes in a Diffusion Model for Social Networks. In: Caires, Lu\’ıs, Italiano, Giuseppe F., Monteiro, Lu\’ıs, Palamidessi, Catuscia, Yung, Moti (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1127–1138. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  15. Kleinberg, J.: The small-world phenomenon: an algorithmic perspective. In: Proc. 32nd ACM Symp. Theory of Computing (2000)

    Google Scholar 

  16. Kramer, A.D.I., Guillory, J.E., Hancock, J.T.: Experimental evidence of massive-scale emotional contagion through social networks. Proceedings of the National Academy of Sciences 111, 8788–8790 (2014)

    Article  Google Scholar 

  17. Meir, A., Moon, J.W.: Relations between packing and covering numbers of a tree. Pacific Journal of Mathematics 61, 225–233 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  18. Mossel, E., Roch, S.: On the submodularity of influence in social networks. In: Proceedings of 39th Annual ACM Symposium on Theory of Computing (STOC) (2007)

    Google Scholar 

  19. Richardson, M., Domingos, P.: Mining knowledge-sharing sites for viral marketing. In: Proceedings of the 8th International Conference on Knowledge scovery and Data Mining (KDD) (2002)

    Google Scholar 

  20. Small, L., Mason, O.: Information diffusion on the iterated local transitivity model of online social networks. Discrete Applied Mathematics 161, 1338–1344 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  21. West, D.B.: Introduction to Graph Theory, 2nd edn. Prentice Hall (2001)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Ryerson University, Toronto, ON, M5B 2K3, Canada

    Anthony Bonato

  2. Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 3J5, Canada

    Jeannette Janssen & Elham Roshanbin

Authors
  1. Anthony Bonato
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  2. Jeannette Janssen
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  3. Elham Roshanbin
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Corresponding author

Correspondence to Anthony Bonato .

Editor information

Editors and Affiliations

  1. Ryerson University, Toronto, Ontario, Canada

    Anthony Bonato

  2. University of California San Diego, La Jolla, California, USA

    Fan Chung Graham

  3. Ryerson University, Toronto, Ontario, Canada

    Paweł Prałat

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© 2014 Springer International Publishing Switzerland

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Bonato, A., Janssen, J., Roshanbin, E. (2014). Burning a Graph as a Model of Social Contagion. In: Bonato, A., Graham, F., Prałat, P. (eds) Algorithms and Models for the Web Graph. WAW 2014. Lecture Notes in Computer Science(), vol 8882. Springer, Cham. https://doi.org/10.1007/978-3-319-13123-8_2

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  • DOI: https://doi.org/10.1007/978-3-319-13123-8_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13122-1

  • Online ISBN: 978-3-319-13123-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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