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Since hubs and authorities only occur for directed networks, we will not calculate them for The Lord of the Rings network. In our class discussion we identified that the ranking of authorities of a directed graph G coincided with eigenvector centrality of the cocitation network of G and that the ranking of hubs coincided with eigenvector centrality of the bibliographic coupling network of G. In doing this we observed that they shared an eigenvalue of (a)-'. Now derive the relationship between the corresponding eigenvectors for hubs and authorities i.e., express the hub eigenvector in terms of the authorities eigenvector. Since hubs and authorities only occur for directed networks, we will not calculate them for The Lord of the Rings network. In our class discussion we identified that the ranking of authorities of a directed graph G coincided with eigenvector centrality of the cocitation network of G and that the ranking of hubs coincided with eigenvector centrality of the bibliographic coupling network of G. In doing this we observed that they shared an eigenvalue of (a)-'. Now derive the relationship between the corresponding eigenvectors for hubs and authorities i.e., express the hub eigenvector in terms of the authorities eigenvector