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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
  • 589 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5354)

Abstract

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.

Keywords

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

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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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