(Quiz week 2, agu 25th) Consider the Network corresponding to the Adjacency Matrix $A$ defined below. 

$ A = \begin{bmatrix} 0 & 1 & 0 & 1 & 0 & 0 & 0\\ 1 & 0 & 1 & 1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0 & 0 & 0 & 0\\ 1 & 1 & 0 & 0 & 0 & 1 & 1\\ 0 & 0 & 0 & 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1 & 1 & 0 & 1\\ 0 & 0 & 0 & 1 & 0 & 1 & 0 \end{bmatrix}$

Build the Network using nodes 1 to 7. Then, for each node $n_ i$, calculate its respective Clustering Coefficient $C_ i$, and then, use them to calculate the Average Clustering Coefficient, $\langle C \rangle$, of the entire Network. Once the calculation is done, state which of the options listed below represents the correct value of $\langle C \rangle$:

1. ~ 0.38.
2. ~ 0.43.
3. ~ 0.48.
4. ~ 0.51.
5. None of the above.

Original idea by: Fábio Assunção.