Question

consider an internet with 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 site b. site d links to a, b, and c. find the importance matrix for the internet (use fractions).

Answer 1

The importance matrix for the given internet can be represented as a table, with each entry representing the fraction of importance that one website gives to another through its outgoing links.

Step-by-step explanation:

The importance matrix for the given internet can be represented as:

abcda01/201/2b1/301/21/3c0100d1/31/31/30

In the matrix, the rows represent the websites that have outgoing links, and the columns represent the websites that have incoming links. The entries in the matrix represent the fraction of importance that a website gives to another website through its outgoing links. For example, site a gives half importance to site b through its outgoing link.

Answer 2

a b c d
a 0/3 1/3 0/3 1/3
b 1/4 0/4 1/4 1/4
c 0/1 1/1 0/1 0/1
d 1/3 1/3 1/3 0/3

To find the importance matrix for the given internet with four websites (a, b, c, and d), we need to determine the importance of each website in terms of the number of other websites that link to it.

Here is the importance matrix for the given internet:

```
a b c d
a 0/3 1/3 0/3 1/3
b 1/4 0/4 1/4 1/4
c 0/1 1/1 0/1 0/1
d 1/3 1/3 1/3 0/3
```
1. Website a has 3 outgoing links (b, d), and out of those 3 websites, 1 links back to a (b), so the importance of a is 1/3.
2. Website b has 4 outgoing links (a, c, d), and none of those 4 websites link back to b, so the importance of b is 0/4.
3. Website c has 1 outgoing link (b), and out of that 1 website, 1 links back to c (b), so the importance of c is 1/1.
4. Website d has 3 outgoing links (a, b, c), and out of those 3 websites, 1 links back to d (b), so the importance of d is 1/3.

Please note that the importance matrix represents the fraction of incoming links to each website compared to the total number of outgoing links from the linking website.