Home / Google PageRank / Exploring PageRank / Dangling Nodes and Cycles

## The Solution of Teleportation

This section is intended to practice the concepts covered in the previous pages by answering a variety of short questions. The APPLET may be a helpful resource (you will need the most recent version of the Java Console installed and enabled to be able to view this Java applet http://java.com/en/download/index.jsp).

### Question 5:

Clearly dangling nodes and cycles cause problems for the random surfer. Once he reaches these sorts of pages he stays there forever and thus never visits other pages, which defeats the purpose of using the frequency of his visits as a tool for ranking pages. Do you have any suggestions to help our trapped random surfer escape from a dangling node or a cycle?

Hint: Most likely you have actually already encountered dangling nodes in your own web surfing. What do you do when you enter a webpage that has no outlinks?

With teleportation, the random surfer can always get out of a sticky situation by jumping to any other node chosen at random.

Let’s think about this teleportation ability for a minute: Approximately what percentage of time do you navigate the Web by using hyperlinks as opposed to typing an address into the URL bar?

The mathematical minds behind Google estimate that you follow hyperlinks about 85% of the time and use the URL bar 15% of the time. They incorporate this into their algorithm to make those actual hyperlinks count more than the artificial teleportation jumps. What would happen if you changed these percentages? Before you experiment with the “chance to follow link” percentage slider bar on the applet, pause to make some predictions.

a. As the “follow link” percentage increases, the actual hyperlinks have much more weight than the artificial teleportation links. As the “follow link” percentage gets closer to 1, do you think the dangling node will increase or decrease in importance? What happens when the “follow link” percentage is 1?

b. What if the “follow link” parameter gets closer to 0? Do you think the dangling node will increase or decrease in importance? True or False: As the “follow link” percentage approaches 0, all pages will have roughly the same PageRank.

c. Change the “follow link” percentage to 25%, 50%, and 75%. Do you expect to see differences in the rankings? As the “follow link” percentage increases from 25% to 75%, do you expect to see more red than green or vice versa on the PageRank histogram of the applet?

Segment 5: from "The Random Surfer" by Tim Chartier on Vimeo.

Segment 6: from "The Random Surfer" by Tim Chartier on Vimeo.