Question

Suppose that we have five websites: A, B, C, D, and E. Let's also suppose that the links between the sites are depicted in the graph below:

Here, the arrow pointing from C to D means that there is a hyperlink on site C that takes you to site D. For small sets of objects, graphs like this one are a convenient way to depict connections.

1. Create a linking matrix L containing the information of which site links to which, just as we did in the popularity example. Remember to normalize, and be sure that your input is exact. (For example, make sure you enter 1/3 instead of 0.3333—this is important for the next part of this exercise, since our columns must sum to 1.) Include all input and output from MATLAB.

2. Use the rref command to find all solutions x to the matrix equation (L - I)x = 0. Include all input and output from MATLAB. If you get an error message, be sure to double-check your answer for the first part of this exercise.

3. Which website has the highest PageRank? Explain your answer, especially in light of any negative numbers that may have appeared in your solutions. List the remaining websites in decreasing PageRank order.

Answer 1

Calculus

Suppose that we have five websites: A, B, C, D, and E. Let's also suppose that the links between the sites are depicted in the graph below:

Here, the arrow pointing from C to D means that there is a hyperlink on site C that takes you to site D. For small sets of objects, graphs like this one are a convenient way to depict connections.

1. Create a linking matrix L containing the information of which site links to which, just as we did in the popularity example. Remember to normalize, and be sure that your input is exact. (For example, make sure you enter 1/3 instead of 0.3333—this is important for the next part of this exercise, since our columns must sum to 1.) Include all input and output from MATLAB.

2. Use the rref command to find all solutions x to the matrix equation (L - I)x = 0. Include all input and output from MATLAB. If you get an error message, be sure to double-check your answer for the first part of this exercise.

3. Which website has the highest PageRank? Explain your answer, especially in light of any negative numbers that may have appeared in your solutions. List the remaining websites in decreasing PageRank order.