Final answer:
The importance matrix represents the connections between websites in a network and is used to analyze the significance of each website.
By assigning fractions to each connection based on the number of links, we can determine the importance of each website within the network.
Step-by-step explanation:
The importance matrix represents the connections between websites in a network and is used to analyze the significance of each website. In this case, we have four websites: A, B, C, and D. Site A links to B and D, site B links to A, C, and D, site C links only to B, and site D links to A, B, and C.
To create the importance matrix, we assign a fraction to each connection based on the number of links from one website to another. For example, since site A links to B and D, we assign a value of 1/2 to each link. Similarly, since site B links to A, C, and D, we assign a value of 1/3 to each link. We repeat this process for all the connections in the network to obtain the importance matrix A:
A = 1/2 1/3 0 1/3
1/3 0 1/3 1/3
0 1 0 0
1/2 1/3 1/3 0