Compute modularity A question from Networks: a introduction

7.8 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 frac- tions were as follows: Womer BlackHispanic White Other Total Black 0.258 0.016 5Hispanic 0.012 0.157 White 0.0130.023 Other0.005 0.007 0.204 0.035 0.0130.323 0.058 0.0190.247 0.306 0.0350.377 0.0240.0160.053 0.423 0.084 5 Hispanic Total 0.289 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 ver- tices as being of four types-black, Hispanic, white, and other-calculate the numbers err and a, that appear in Eq. (7.76) for each type. Hence calculate the modularity of the network with respect to ethnicitv