Preferential attachment in sexual networks

Abstract

Many social networks are characterized by a highly uneven distribution of links. The observed skewed distributions have in several cases been attributed to preferential attachment (PA), a tendency among nodes in a growing network to form new links preferentially to nodes with high numbers of links. We test the PA conjecture in sexual contact networks. A maximum likelihood estimation-based expectation-maximization fitting technique is used to model new partners over a 1-year period based on the number of partners in foregoing periods of 2 years, 4 years, and lifetime. The PA model is modified to account for individual heterogeneity in the inclination to find new partners and fitted to Norwegian survey data on heterosexual men and women. Results show evidence of nonrandom, sublinear PA when comparing the growth in 3-to 5-year periods. The potential implications of these findings are discussed.sexual behavior ͉ sexually transmitted diseases I n comparison with the observed incidence of sexually transmitted infections in modern societies, the average number of sexual contacts in national populations is surprisingly low. It has been suggested that the endemic and epidemic spread is driven by smaller subsets (core groups) of the population, in which members have significantly higher numbers of partners and a preference for selecting partners within the group (1). Several studies have, however, recently reported a highly skewed distribution of sexual contacts without a clear core group.The tail of the sex partner distribution is often modeled by a simple power law, that is, the probability mass function (pmf) of sexual partners P( j) have the functional form P( j) Ϸ Cj Ϫ␥ for some excess j Ͼ j t , where C and ␥ are positive constants. The first suggestion of power law scaling was published by Colgate et al. (2) in 1989 from data on homosexual men seen at a sexually transmitted infection clinic in London. More recently, Liljeros et al. (3) observed a power law in population data from Sweden, which was later supported by population studies in Burkina Faso (4), Uganda and the United States (5), and Britain and Zimbabwe (6). With one exception (women from the Rakai district in Uganda), the reported slopes are close to ␥ ϭ 3; the range for men being 2.8 Յ ␥ Յ 5.4 and the range for women being 3.0 Յ ␥ Յ 4.2.The finding of a power law has been subject to some controversy, and the question has been raised whether a power-law function adequately fits the data. The available sexual data are limited, and the published studies reveal power-law scaling of over one to two orders of magnitude. The limited scaling regime is not sufficient to distinguish a power law from other heavy-tailed distributions, such as log-normal or stretched exponential (Weibull), both of which have characteristic scales and curve away with exponential decay for large enough j. A study by Handcock (7) suggests that a log-normal distribution provides the best description of the data when lower numbers of partners are included.Here, we address the question o...

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