Using Tutte polynomials to characterize sexual contact networks

Abstract

Tutte polynomials are used to characterize the dynamic and topology of the sexual contact networks, in which pathogens are transmitted as an epidemic. Tutte polynomials provide an algebraic characterization of the sexual contact networks and allow the projection of spread control strategies for sexual transmission diseases. With the usage of Tutte polynomials, it allows obtaining algebraic expressions for the basic reproductive number of different pathogenic agents. Computations are done using the computer algebra software Maple, and it’s GraphTheory Package. The topological complexity of a contact network is represented by the algebraic complexity of the correspondent polynomial. The change in the topology of the contact network is represented as a change in the algebraic form of the associated polynomial. With the usage of the Tutte polynomials, the number of spanning trees for each contact network can be obtained. From the obtained results in the polynomial form, it can be said that Tutte polynomials are of great importance for designing and implementing control measures for slowing down the propagation of sexual transmitted pathologies. As a future research line, the analysis of weighted sexual contact networks using weighted Tutte polynomials is considered.