Ranking web wage

3 Ranking web pages (25 marks) Let's have a look at how search engines like Google go about ranking webpages to decide in which order to display all those pages containing the term that you are looking for. Here is a picture of a toy version of the world wide web consisting of eight pages. Whenever a page points to another page via a hyperlink this is indicated by an arrow. In this problem set I've highlighted all the things you are supposed to do in bold. Let ri denote the rank of page i, that is, r is a nonnegative number that measures the importance of this page. Here are some properties (with increasing sophistication) which our ranking should have: 1. The more pages link to a page the larger its ranking should be (roughly). 2. Being linked to by a low-ranking page should contribute less to the ranking of a page than being linked to by a high-ranking page. 3. A page containing a lot of hyperlinks should contribute less to the ranking of any page it links to than a page that contains few hyperlinks. Let's turn our ranking problem into maths. As in the previous set of problems, we capture our miniweb/graph in the form of an adjacency matrix. If page i is linked to from page j then the ijth entry of our matrix is 1, otherwise it is 0. Since our miniweb has eight pages our matrix wll be an 8 x 8 matrix This diagram) is a directed graph. Unlike the graphs we considered in the previous set of problems the edges of a directed graph all have a direction. We only note that directed graphs can be analyzed using the same linear algebra techniques as undirected graphs. 3 Ranking web pages (25 marks) Let's have a look at how search engines like Google go about ranking webpages to decide in which order to display all those pages containing the term that you are looking for. Here is a picture of a toy version of the world wide web consisting of eight pages. Whenever a page points to another page via a hyperlink this is indicated by an arrow. In this problem set I've highlighted all the things you are supposed to do in bold. Let ri denote the rank of page i, that is, r is a nonnegative number that measures the importance of this page. Here are some properties (with increasing sophistication) which our ranking should have: 1. The more pages link to a page the larger its ranking should be (roughly). 2. Being linked to by a low-ranking page should contribute less to the ranking of a page than being linked to by a high-ranking page. 3. A page containing a lot of hyperlinks should contribute less to the ranking of any page it links to than a page that contains few hyperlinks. Let's turn our ranking problem into maths. As in the previous set of problems, we capture our miniweb/graph in the form of an adjacency matrix. If page i is linked to from page j then the ijth entry of our matrix is 1, otherwise it is 0. Since our miniweb has eight pages our matrix wll be an 8 x 8 matrix This diagram) is a directed graph. Unlike the graphs we considered in the previous set of problems the edges of a directed graph all have a direction. We only note that directed graphs can be analyzed using the same linear algebra techniques as undirected graphs