I need help understanding what the questions want me to do$.$ the first question I know I build a graph. Q$1$Provide a java function that builds a graph with n$^2$ vertices labeled i $=0,1,..,$ n$^2-1,$ and each vertex i has $4$ neighbors labeled

$($i $-1+$ n$^2)$ mod n$^2,$

$($i $+1+$ n$^2)$ mod n$^2,$

$($i $-$ n $+$ n$^2)$ mod n$^2,$

$($i $+$ n $+$ n$^2)$ mod n$^2$ Q$2.$ using that graph i have to make an induced graph where each vertice has a $50\%$chance of being selected.edge in induced graph exits only if both vertices were selected from the original graph, does this $,$if vertices $2,4,5,8$ were selectedin the induce graph there is an edge between them now? Q$3.$ asks us to Provide a function that returns the largest $($the most vertices$)$component of graph I which is from the induced graph we just made $,$ what exactly does this mean $,$ what kind of out put would i be looking for. ill shows pics because i cant figure out if i am getting the correct answer for the largest component part Original Graph:

$0$:$,8,1,6,3$

$1$:$,0,2,7,4$

$2$:$,1,3,8,5$

$3$:$,2,4,0,6$

$4$:$,3,5,1,7$

$5$:$,4,6,2,8$

$6$:$,5,7,3,0$

$7$:$,6,8,4,1$

$8$:$,7,0,5,2$

Induced Graph:

$1$: $0274$

$3$: $2406$

$5$: $4628$

$6$: $5730$

Largest Subgraph:

$1$: $0274$