The following is a toy web graph with hubs C, D, E and F, and authorities A, B, and G.  

a) Show the (hubs and authorities) values obtained by running two rounds of the hubs and authorities algorithm on this network. Show the values both before and after the final normalization step, in which we divide each authority score by the sum of all authority scores, and divide each hub score by the sum of all hub scores. You should express the normalized scores as fractions rather than decimals. 

 

b) Suppose you wish to add a new authority web site X to the network and want it to have as high an authority score as possible. You also have the ability add another new hub web site Y which we can use as a hub to elevate the score of X. Consider the following three options:

• You add a link from Y to X (and add no other new links).
• You add a link from Y to A and X (and no other links).
• You add a link from Y to A, B, G and X (and no other new links).

For each option, show the normalized authority values that each of A, B, G and X obtain when you run 2-steps of hub-authority computation on the resulting network (as you did in part (a)). Which option gives X the highest (normalized) score?

D E F A B G