Graph Theory: Betweenness and Closeness Centrality?

Posted on 2017-10-17 17:29:00 in Math by MADDY

1. Your younger brother has just transferred to a new secondary school. There are a bunch of 
popular students in his class, the “kewl kidz”: everyone in class is friends with at least one kewl 
kid, and the kewl kids are all friends with each other. Having peeked at your notes for Statistics Module, 
he thinks it’s a good idea to befriend the leader of the kewl kidz, Amos. He only manages to 
befriend Amos in the first week of school. 
Consider the network whose vertices are made up of students in his class, and an edge represents 
friendship between students. What is your brother’s betweenness centrality in this network just 
after one week in the new school? 
(A) 0 
(B) 1 
(C) Between 0 and 1 
(D) Cannot be deduced from the given information 

2. Putting your knowledge gained in Statistics Module to good use, you subsequently calculate the “Amos 
number” of every student in your brother’s class. This is the distance of the student from Amos in 
the network described in the previous question. Without doing further calculations, we can 
conclude that: 
Ccen(brother) ___ Ccen(Amos) 
(A) < 
(B) = 
(C) > 
(D) None of the above can be deduced from the given information.

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