Tutte Polynomials and Topological Quantum Algorithms in Social Network Analysis for Epidemiology, Bio-surveillance and Bio-security

  • Mario Vélez
  • Juan Ospina
  • Doracelly Hincapié
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5354)


The Tutte polynomial and the Aharonov-Arab-Ebal-Landau algorithm are applied to Social Network Analysis (SNA) for Epidemiology, Biosurveillance and Biosecurity. We use the methods of Algebraic Computational SNA and of Topological Quantum Computation. The Tutte polynomial is used to describe both the evolution of a social network as the reduced network when some nodes are deleted in an original network and the basic reproductive number for a spatial model with bi-networks, borders and memories. We obtain explicit equations that relate evaluations of the Tutte polynomial with epidemiological parameters such as infectiousness, diffusivity and percolation. We claim, finally, that future topological quantum computers will be very important tools in Epidemiology and that the representation of social networks as ribbon graphs will permit the full application of the Bollobás-Riordan-Tutte polynomial with all its combinatorial universality to be epidemiologically relevant.


Social Network Analysis Tutte Polynomial Aharonov-Arab-E bal-Landau algorithm Topological Quantum Computation Basic Reproductive Number Borders 


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  1. 1.
    World Health Organization. The World Health Report 2007. A safer future: global public health security in the 21st century, Geneva (2007)Google Scholar
  2. 2.
    Eubank, S., Guclu, H., Kumar, A., et al.: Modelling disease outbreaks in realistic urban social networks. Nature 429, 180–184 (2004)CrossRefGoogle Scholar
  3. 3.
    Chen, Y.-D., Tseng, C., King, C.-C., Wu, T.-S.J., Chen, H.: Incorporating Geographical Contacts into Social Network Analysis for Contact Tracing in Epidemiology: A Study on Taiwan SARS Data. In: Zeng, D., Gotham, I., Komatsu, K., Lynch, C., Thurmond, M., Madigan, D., Lober, B., Kvach, J., Chen, H. (eds.) BioSurveillance 2007. LNCS, vol. 4506, pp. 23–36. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Bollobás, B., Riordan, O.: A polynomial invariant of graphs on orientable surfaces. Proc. London Math. Soc. 83(3), 513–531 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Aharonov, D., Arad, I., Eban, E., Landau, Z.: Polynomial Quantum Algorithms for Additive aproximations of the Potts model and other Points of the Tutte Plane. In: QIP 2007, Australia (2007) arXiv:quant-ph/070208Google Scholar
  6. 6.
    Guyer, T.: Stratum and Compactness Maplet (December 2007),
  7. 7.
    Champanerkar, A., Kofman, I., Stolzfus, N.: Quasi-tree expansion for the Bollobás-Riordan-Tutte polynomial (2007) arXiv:0705.3458v1Google Scholar
  8. 8.
    Hincapié, D., Ospina, J.: Spatial Epidemia Patterns Recognition using Computer Algebra. In: Zeng, D., Gotham, I., Komatsu, K., Lynch, C., Thurmond, M., Madigan, D., Lober, B., Kvach, J., Chen, H. (eds.) BioSurveillance 2007. LNCS, vol. 4506, pp. 216–221. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Jaeger, F., Vertigan, D.L., Welsh, D.J.A.: On the computational complexity of the Jones and Tutte polynomials. Mathematical Proceedings of the Cambridge Philosophical Society 108, 35–53 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Mario, V., Juan, O.: Possible quantum algorithms for the Bollobas- Riordan-Tutte polynomial of a ribbon graph. In: Donkor, E.J., Pirich, A.R., Brandt, H.E. (eds.) Proceedings of SPIE, March 27, 2008. Quantum Information and Computation VI, vol. 6976, pp. 697–60 (2008)Google Scholar
  11. 11.
    Tucci, R.R.: Use of a Quantum Computer and the Quick Medical Reference To Give an Approximate Diagnosis (2008) arXiv:0806.3949Google Scholar
  12. 12.
    Bodkin, P., Sherman, W.: Graph Analysis Maplet (November 2004),

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Mario Vélez
    • 1
  • Juan Ospina
    • 1
  • Doracelly Hincapié
    • 2
  1. 1.Logic and Computation Group Physical Engineering Program School of Sciences and HumanitiesEAFIT UniversityMedellinColombia
  2. 2.Epidemiology Group National School of Public HealthUniversity of AntioquiaMedellinColombia

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