Opportunity and choice in social networks
  Our societies are heterogeneous in many dimensions such as census, education, religion, ethnic and cultural composition. The links between individuals - e.g. by friendship, marriage or collaboration - are not evenly distributed, but rather tend to be concentrated within the same group. This phenomenon, called `imbreeding homophily', has been related to either (social) preference for links with own-type individuals (`choice-based' homophily) or to the prevalence of individuals of her same type in the choice set of an individual (`opportunity-based' homophily). Choices determine the network of relations we observe whereas opportunities pertain to the composition of the (unobservable) social network individuals are embedded in and out of which their network of relations is drawn. In this view, we propose a method that, in the presence of multiple data, allows one to distinguish between opportunity and choice based homophily. The main intuition is that, with unbiased opportunities, the effect of choice-based homophily gets weaker and weaker as the size of the minority shrinks, because individuals of the minority rarely meet and have the chance to establish links together. The occurrence of homophily in the limit of very small minorities is therefore an indicator of opportunity bias. We test this idea across the dimensions of race and education on data on US marriages, and across race on friendships in US schools. 
P. Pin, M. Marsili, S. Franz