Degree Distributions of Sexual Networks: Should We Buy Scale Free?

Deven Hamilton, University of Washington
Mark S. Handcock, University of Washington

The degree distribution is a fundamental characteristic of any network and a focus of research on STI transmission. When the degree distribution has high variance the level of infectivity requisite for a disease to generate an epidemic is close to zero and the critical vaccination fraction approaches unity. Many authors have focused attention on so-called "scale free" distributions - a set with power law tail behavior and sometimes infinite variance. Given the potential policy implications, claims of infinite variance degree distributions merit further scrutiny. Prior analyses have underestimated the amount of error in the tail of the distribution, ignored social process in favor of simple curve fitting and assumed random mixing despite empirical evidence to the contrary. We test the fit of 11 models to five nationally representative samples of the US. Our results indicate social process models fit the observed demographic information as well or better than scale-free models.