These are the papers I referred to at Bright Club:
The Web of Human Sexual Contacts: this paper was published in Nature in 2001 (the link is to a preprint version). The authors analysed a 1996 Swedish survey of sexual behaviour (2810 respondents) and found that the number of sexual partners reported, both in the short term (12 months prior to survey) and long term (lifetime), varied according to a power law. This means that most people haven’t had that many sexual partners, a few people have had a few more, but a very small number of people have had very many partners; in the picture on the Wikipedia page (showing an idealised power law distribution), the x-axis would represent number of sexual partners, and the y-axis the cumulative distribution (i.e. as you go up the y-axis, you see more and more people having had a smaller number of partners). When plotted on a log-log scale (linked-to graph shows example simulated data), the curve becomes a straight line with a negative gradient – the gradient is the exponent of the power law. This kind of network is called scale-free, because whatever scale you consider the network at, its statistics are similar.
The small number of people with a very large number of connections to others are referred to as network ‘hubs’, analogous to a transport hub, as disparate parts of the network are linked up through them. Knowing the structure of a sexual network is very important for targeting effective interventions dealing with the spread of sexually transmitted infections, so this research has serious implications for public health policy. An important feature of scale-free networks is their resilience against random ‘node deletions’: removing a random person from the sexual network (I know what you’re thinking – no, not in any sinister way) will have very little effect on how disease spreads. However, by specifically targeting the network hubs, disease spread can be reduced dramatically just by influencing a small number of hub people, simultaneously reducing cost and improving efficacy. The trick is successfully identifying your hub nodes…
Hubs are also a frequent (though not defining) feature in small-world networks.
Sexual network analysis of a gonorrhoea outbreak: analysis of a gonorrhoea outbreak using network theory. The authors trace the initial spread to patrons frequenting a certain motel bar in Alberta, which they don’t actually name in the paper presumably for legal reasons. The main interesting findings were that cheaper network analysis methods could be used instead of standard case-control analysis to arrive at similar results, including the identification of the causal link between several seemingly isolated disease outbreaks.
Chains of Affection: analysis of a high-school “romance network”. This revealed a very different network structure, with long chains of links between students rather than clear hubs, with obviously different implications for STI spread through the network. The authors suggest the different structure arises from the social rules that operate at high-school: not dating your friend’s ex, for example.
*not really. Probably.