Science:Math Exam Resources/Courses/MATH307/April 2013/Question Section 201 06 (c)

MATH307 April 2013

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Question Section 201 06 (c)
Consider the same graph as in the previous question, now interpreted as an internet where the vertices represent web pages and the arrows represent links. (c) Starting with equal probabilities for each page, what are the probabilities of being on each page after one step (with α = 1/2)? Based on this calculation, which page has the highest rank?

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. ${\begin{aligned}{\underline {x_{1}}}&=S{\underline {x_{0}}}\\&={\begin{bmatrix}1/12&1/12&1/12&1/12&1/12&1/6\\1/3&1/12&1/12&1/12&1/12&1/6\\1/12&1/3&1/12&1/12&1/12&1/6\\1/3&1/12&1/12&1/12&1/12&1/6\\1/12&1/3&1/12&7/12&1/12&1/6\\1/12&1/12&7/12&1/12&7/12&1/6\end{bmatrix}}{\begin{bmatrix}1/6\\1/6\\1/6\\1/6\\1/6\\1/6\end{bmatrix}}\\&=(1/72){\begin{bmatrix}7\\10\\10\\10\\16\\19\end{bmatrix}}\end{aligned}}$ From this solution, it is clear that the page with the highest rank after one step is page 6.