Problem $2$: PageRank $(10\%)$

In this problem you will do some PageRank computations for the following graph:

You can implement this in Python or do the computations by hand. In order to receive

full credit show your computations or add the $($relevant$)$ code and output to your written

answer.

$2\mathrm{.}1$ Compute the PageRank of each page $(a,b,c)$ assuming no teleportation$/$taxation $($aka

set $=0$ in the original$/$recursive pagerank equation$)$ with $=0\mathrm{.}85.$

$2\mathrm{.}2$ Compute the PageRank of each page $(a,b,c)$ again assuming $=0\mathrm{.}85.$ Note that we

have two PageRank versions, the vanilla $($ is a free parameter$)$ and the probabilistic

version $(=\frac{1-}{n}).$ Let's use the probabilistic version here $($so we don't have to worry

about how to set $).$

$2\mathrm{.}3$ Provide the data representation for the edge list, adjacency list, and adjacency matrix

for the example graph above.

$2\mathrm{.}4$ Which data representation $($edge list, adjacency list, or adjacency matrix$)$ would you

use for the actual webgraph ${?}^2?$

Consider both storage and runtime efficiency for computing PageRank.

State the storage requirement for a general webgraph in terms of the number of pages

$n$ and the number of links $m$ for your selected data structure.