Exercise $2(4$ pts$)$Network Science

HW$-2(12$ pts$)$

Exercise $1(8$ pts$)$

Consider the directed graph on the right and take

the jumping probability $=0\mathrm{.}3.$ Answer the

following questions about PageRank for this

graph $(2$ points for each correct answer$).$

What is the matrix $P$ for the random walk on the graph?

What is the matrix $P_1$ corresponding the first step of adjustment?

What is the matrix $P_2$ corresponding to the second step of adjustment?

Which of the following vectors is a stationary distribution vector for $P_2?$

a$.(0\mathrm{.}4706,0\mathrm{.}2647,0\mathrm{.}2647)$

b$.(0\mathrm{.}2647,0\mathrm{.}4706,0\mathrm{.}2647)$

c$.(0\mathrm{.}2647,0\mathrm{.}2647,0\mathrm{.}4706)$

d$.(0\mathrm{.}2647,0\mathrm{.}4706,0\mathrm{.}4706)$

e$.(0\mathrm{.}4706,0\mathrm{.}2647,0\mathrm{.}4706)$

f$.(0\mathrm{.}4706,0\mathrm{.}4706,0\mathrm{.}2647)$