In the basic six-degrees-of-separation question, one asks whether most pairs of people in the world are...

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In the basic six-degrees-of-separation question, one asks whether most pairs of people in the world are connected by a path of at most six edges in the social network, where an edge joins any two people who know each other on a first-name basis. Now let's consider a variation on this question. For each person in the world, we ask them to rank the thirty people they know best, in descending order of how well they know them. (Let's suppose for purposes of this question that each person is able to think of thirty people to list.) We then construct two different social networks: a) The "close-friend" network: from each person we create a directed edge only to their ten closest friends on the list. b) The "distant-friend" network: from each person we create a directed edge only to the ten people listed in positions 21 through 30 on their list. Let's think about how the small-world phenomenon might differ in these two networks. In particular, let C be the average number of people that a person can reach in 6 steps in the close-friend network, and D be the average number of people that a person can reach in six steps in the distant-friend network (taking average of all people in the world). When researchers have done empirical studies to compare these two types of networks (and the exact details differ from one study to another) they tend to find that one of C or D is consistently larger than the other. Which of the two quantities, C or D do you expect to be larger? Give brief explanation to your answer. (2 points) In the basic six-degrees-of-separation question, one asks whether most pairs of people in the world are connected by a path of at most six edges in the social network, where an edge joins any two people who know each other on a first-name basis. Now let's consider a variation on this question. For each person in the world, we ask them to rank the thirty people they know best, in descending order of how well they know them. (Let's suppose for purposes of this question that each person is able to think of thirty people to list.) We then construct two different social networks: a) The "close-friend" network: from each person we create a directed edge only to their ten closest friends on the list. b) The "distant-friend" network: from each person we create a directed edge only to the ten people listed in positions 21 through 30 on their list. Let's think about how the small-world phenomenon might differ in these two networks. In particular, let C be the average number of people that a person can reach in 6 steps in the close-friend network, and D be the average number of people that a person can reach in six steps in the distant-friend network (taking average of all people in the world). When researchers have done empirical studies to compare these two types of networks (and the exact details differ from one study to another) they tend to find that one of C or D is consistently larger than the other. Which of the two quantities, C or D do you expect to be larger? Give brief explanation to your answer. (2 points)