Question

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1. In particular, suppose you wanted to create a new Web page X, and add it to the network in the above network, so that it could achieve a (normalized) authority score that is as large as possible. One thing you might try is to create a second page Y as well, so that Y links to X and thus confers authority on it. In doing this, it's natural to wonder whether it helps or hurts X's authority to have Y link to other nodes as well.

Specifically, suppose you add X and Y to the network in the above network. In order to add X and Y to this network, one needs to specify what links they will have. Here are two options; in the first option, Y links only to X, while in the second option, Y links to other strong authorities in addition to X.

For each of these two options, we'd like to know how X fares in terms of its authority score. So, for each option, show the normalized authority values that each of A, B, and X get when you run the 2-step hub-authority computation on the resulting network (as in part (a)). (That is, you should perform the normalization step where you divide each authority value down by the total.)

For which of Options 1 or 2 does page X get a higher authority score (taking normalization into account)? Give a brief explanation in which you provide some intuition for why this option gives X a higher score.

• Option 1: Add new nodes X and Y to the above network; create a single link from Y to X; create no links out of X.
• Option 2: Add new nodes X and Y to the above network; create links from Y to each of A, B, and X; create no links out of X.

2. Suppose instead of creating two pages, you create three pages X, Y , and Z, and again try to strategically create links out of them so that X gets ranked as well as possible.

Describe a strategy for adding three nodes X, Y , and Z to the network in the above network, with choices of links out of each, so that when you run the 2-step hub-authority computation (as in parts (a) and (b)), and then rank all pages by their authority score, node X shows up in second place.

(Note that there's no way to do this so that X shows up in first place, so second place is the best one can hope for using only three nodes X, Y , and Z.)

Here is the picture to solve this two questions:

Answer 1

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