Problem $3[60$ points$]$: Given the following graph with nodes A$,$B$,$C$,$D$,$E$,$F$,$G$,$H and the

following directed edges: $,$

$(E,C),(F,C),(F,H),(G,A),(G,C),(H,A).$

$1-$ Perform $4$ iterations of the HITS algorithm and list the resulting $H$ and A for each

mode. Start with all a$\text{'}$s and h$\text{'}$s $=1.$

$2-$ Perform $4$ iterations of the PageRank algorithm and list the resulting PageRank for

each node. Start with all PR$=1$