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Exercise 3 . A food chain is a directed graph with n nodes. The directed edges go from 1 to 2 , 2 to 3
Exercise A food chain is a directed graph with nodes. The directed edges go from to
to to and so on
a What are the degree centralities of nodes dotsn Remember that for a directed graph,
degree centrality is usually identified with
b What are the eigenvalue centralities of nodes dotsn Explain your answer.
c Now calculate the Katz centralities of each node. Hint: it is easier to start with the
definition of Katz centrality, than the matrix inversion formula that we derived in class. Your
answer will depend on the parameter
d Optional question In class we determined that the Katz centrality is defined for
where is the largest real eigenvalue of What is the condition for in the Katz centrality
calculation you did in part c Explain why can be arbitrarily large for this network.
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