Social networks involve interactions (connections) between members of the network. Sociologists define network density as the ratio of actual network connections to the number of possible one-to-one connections. For example, a network with 10 members has (10 2) = 45 total possible connections. If that network has only 5 connections, the network density is 5/45 = .111. Sociologists at the University of Michigan assumed that the density x of a social network would follow a uniform distribution between 0 and 1 (Social Networks, 2010).
a. On average, what is the density of a randomly selected social network?
b. What is the probability that the randomly selected net-work has a density higher than .7?
c. Consider a social network with only 2 members. Explain why the uniform model would not be a good approximation for the distribution of network density.