Question
Example 1: Consider five webpages A, B, C, D and E that link t0 each other accordling to the graph below . For iuslance_ the arrow [rOm A to € indicates that page links to page C and the Lwo-way arrow belween and B iudicales Lhat and B link t0 each other.The PageRank algorithmn assigus ranks r(A) "(B), r(C). r(D); and r(E) that are all between and (inclusive) and SuIn toEach page equally distributes its Own PageRank along its outbound links. For example. page B has two outbound links_ S0
Example 1: Consider five webpages A, B, C, D and E that link t0 each other accordling to the graph below . For iuslance_ the arrow [rOm A to € indicates that page links to page C and the Lwo-way arrow belween and B iudicales Lhat and B link t0 each other. The PageRank algorithmn assigus ranks r(A) "(B), r(C). r(D); and r(E) that are all between and (inclusive) and SuIn to Each page equally distributes its Own PageRank along its outbound links. For example. page B has two outbound links_ S0 page B ~donates" 2H to both page and page D_ Page D also gives hall its PageRank t0 page S0 the PageRank of salisfies: r(A) = 4(B) "D) Since page B has inbound links [rom page (which has four total outbound links) and page (which has two total outbound links) , the PageRank of page B salisfies: r(B) = 44 "CL The Iull list of equations is: r(A) = % r(D) r(B) = 4 'C) r(C) = 4 {(B) r(D) = 4 +r(E) r(E) = 4 r(C)
Answers
A content map can be used to show how different pages on a website are connected. For example, the following content map shows the relationship among the five pages of a certain website with links between pages represented by arrows. (GRAPH CANT COPY) The content map can be represented by a 5 by 5 adjacency matrix where each entry, $a_{i j},$ is either 1 (if a link exists from page $i$ to page $j$ ) or 0 (if no link exists from page $i$ to page $j$ ). (a) Write the 5 by 5 adjacency matrix that represents the given content map. (b) Explain the significance of the entries on the main diagonal in your result from part (a). (c) Find and interpret $A^{2}$
So what? We see her for part? A. We get that if someone visited the page a the Web page a then they also visited Web page beat. Okay, so this is reflexive because obviously, if you visited Web page A then you visited, you still visited Web page A. So that's still reflexive. And then we also see that it's transitive because if you visited a, um, that means you visited B And then let's say you visited B and that implies that you visited, See, then if you visited a you must have visited see. So for that reason it is transitive than for part B, this one would be considered symmetric. We see that since there are no common links found on A and B, um, we see that there are no common links found on both B and A so because we say a, uh, be no common links. We can also say that the A no common links. So by switching those and resulting in the same thing, we see that this one is symmetric. Then see is also gonna be symmetric. There is one common link, so a B one common link That means that be? And they also have one common link. Then s O that one's gonna be symmetric. And then lastly, we have that the Web page includes links to both Web page A and B so a and be, um, share links. So that means that DNA are gonna share links, and that ultimately means that this one is going to be symmetric a swell.