In a survey of couples in the US city of San Francisco, Catania et al. [65] recorded, among other things, the ethnicity of their interviewees and calculated the fraction of couples whose members were from each possible pairing of ethnic groups. The fractions were as follows:
Assuming the couples interviewed to be a representative sample of the edges in the undirected network of relationships for the community studied, and treating the vertices as being of four types-black, Hispanic, white, and other-calculate the numbers err and a r that appear in Eq. (7.76) for each type. Hence calculate the modularity of the network with respect to ethnicity.
