Consider the directed network G = (V,E) with N = 5 nodes and L = 8 links, in which node 1 points to nodes 2 and 3, node 2 points to node 4, node 3 points to nodes 2 and 4, node 4 points to node 2, and node 5 points to nodes 3 and 4. (f) State the definition of the Katz centrality. Calculate the Katz centrality ; of each node of the network and rank the nodes, from the most to the least central, according to their Katz centrality. Do you get a different ranking from that obtained based on the eigenvector centrality? Explain why.

Advanced Engineering Mathematics
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Consider the directed network G = (V,E) with N = 5 nodes and L = 8 links, in which
node 1 points to nodes 2 and 3, node 2 points to node 4, node 3 points to nodes 2 and
4, node 4 points to node 2, and node 5 points to nodes 3 and 4.
(f) State the definition of the Katz centrality. Calculate the Katz centrality ; of each
node of the network and rank the nodes, from the most to the least central,
according to their Katz centrality. Do you get a different ranking from that
obtained based on the eigenvector centrality? Explain why.
Transcribed Image Text:Consider the directed network G = (V,E) with N = 5 nodes and L = 8 links, in which node 1 points to nodes 2 and 3, node 2 points to node 4, node 3 points to nodes 2 and 4, node 4 points to node 2, and node 5 points to nodes 3 and 4. (f) State the definition of the Katz centrality. Calculate the Katz centrality ; of each node of the network and rank the nodes, from the most to the least central, according to their Katz centrality. Do you get a different ranking from that obtained based on the eigenvector centrality? Explain why.
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