45 total possible connections. If that network has 2) nly 5 connections, the network density is 5/45 = .111. ociologists at the University of Michigan assumed that the ensity x of a social network would follow a uniform distri- ution between 0 and 1 (Social Networks, 2010). - On average, what is the density of a randomly selected social network? What is the probability that the randomly selected net-

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5.14 Social network densities. Social networks involve inter-
actions (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
()-
C) = 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 distri-
bution 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 approxi-
mation for the distribution of network density.
Transcribed Image Text:5.14 Social network densities. Social networks involve inter- actions (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 ()- C) = 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 distri- bution 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 approxi- mation for the distribution of network density.
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