Problem $3(2$ points$)$

In the directed graph shown in Figure $2,$ a set of web pages with links between

some of them is depicted.

$($a$)$ Which set of nodes is in the largest strongly connected component

$($SCC$)$ in this graph? $(0\mathrm{.}5$ point$)$

$($b$)$ Which nodes are upstream of the largest SCC$?(0\mathrm{.}5$ point$)$

$($c$)$ Which nodes are downstream of the largest SCC$?(0\mathrm{.}5$ point$)$

$($d$)$ Now suppose you could add a single link to the graph from a node A

to a node B$.$ You want to choose this link to make the largest strongly

connected component as large as possible. Explain your answer. $(0\mathrm{.}5$

point$)$ Problem $3(2$ points$)$

In the directed graph shown in Figure $2,$ a set of web pages with links between some of them is depicted.

$($a$)$ Which set of nodes is in the largest strongly connected component $($SCC$)$ in this graph? $(0\mathrm{.}5$ point$)$

$($b$)$ Which nodes are upstream of the largest SCC$?(0\mathrm{.}5$ point$)$

$($c$)$ Which nodes are downstream of the largest SCC$?(0\mathrm{.}5$ point$)$

$($d$)$ Now suppose you could add a single link to the graph from a node A to a node B$.$ You want to choose this link to make the largest strongly connected component as large as possible. Explain your answer. $(0\mathrm{.}5$ point$)$

Figure $2$: Web network