i) Compute the hub and authorities scores for all nodes. ii) Does this graph contain spider traps? Dead ends? If so, which nodes.

Formulation of link matrix.

L = $\left[\begin{matrix} 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 & 1 & 1 \\ 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 \end{matrix}\right]$

$L^T = \left[\begin{matrix} 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 1 & 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 1 \end{matrix}\right]$

H = Hub score

A = Authority score.

Iteration 1:

Initialize h to 1

$h = \left[\begin{matrix} 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ \end{matrix}\right]$

calculate $ a = L^Th$ and scale

$a = \left[\begin{matrix} 1 \\ 2 \\ 3 \\ 1 \\ 0 \\ 1 \\ 2 \\ \end{matrix}\right]$After scaling $a = \left[\begin{matrix} 1/3 \\ 2/3 \\ 1 \\ 1/3 \\ 0 \\ 1/3 \\ 2/3 \\ \end{matrix}\right]$

calculate h = La and scale down

$h = \left[\begin{matrix} 2/3 \\ 1 \\ 1/3 \\ 4/3 \\ 5/3 \\ 1 \\ 2/3 \\ \end{matrix}\right]$After scaling $h = \left[\begin{matrix} 2/5 \\ 3/5 \\ 1/5 \\ 4/5 \\ 1 \\ 3/5 \\ 2/5 \\ \end{matrix}\right]$

Iteration 2:

Calculate $ = L^Th$ and scale down.

$a = \left[\begin{matrix} 4/5 \\ 7/5 \\ 11/5 \\ 1/5 \\ 0 \\ 4/5 \\ 6/5 \\ \end{matrix}\right]$After scaling $a = \left[\begin{matrix} 4/11 \\ 7/11 \\ 1 \\ 1/11 \\ 0 \\ 4/11 \\ 6/11 \\ \end{matrix}\right]$

Calculate h = La and scale down.

$h = \left[\begin{matrix} 7/11 \\ 1 \\ 1/11 \\ 14/11 \\ 18/11 \\ 1 \\ 6/11 \\ \end{matrix}\right]$After scaling $h = \left[\begin{matrix} 7/18 \\ 11/18 \\ 1/18 \\ 14/18 \\ 1 \\ 11/18 \\ 6/18 \\ \end{matrix}\right]$

Spider Trap: Yes

1. A - B - C - D

2. C - D - F

Dead Ends: Yes

Node G is dead end.