Centrality and AIDS

In the case of the “has sex with” relation, the degree of an actor is simply the number of people she has sex with. Suppose the probability of something occurring to an actor is a function of the number of exposures she has to it. For example, suppose the probability of adoption of an innovation is a function of the number of friends that a person witnesses adopting. Then we can interpret degree centrality in a friendship network as an index of the probability that they will adopt the innovation. All else being equal, then, we can describe degree centrality as measuring the risk (or opportunity) of receiving whatever is flowing through the network.