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Social network densities. Social networking sites for
Chapter 4, Problem 145E(choose chapter or problem)
Problem 145E
Social network densities. Social networking sites for business professionals are used to promote one’s business. Each social network involves interactions (connections) between members of the network. Researchers 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 = 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 network 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.
Questions & Answers
QUESTION:
Problem 145E
Social network densities. Social networking sites for business professionals are used to promote one’s business. Each social network involves interactions (connections) between members of the network. Researchers 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 = 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 network 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.
ANSWER:
Step 1 of 6
(a)
Find the average density of a randomly selected social network.
Define the random variable x as the density of the social network that follows a uniform distribution between 0 and 1. The mean of the uniform distribution is computed using the formula given below:
Substitute c as 0 and d as 1.
Thus, the average density of a randomly selected social network is 