Exercise $4.$ A network with $7$ nodes, labeled $1,2,$dots$7$ has an adjacency matrix:

$A=([0,1,1,0,0,0,0],[1,0,0,1,0,0,0],[1,0,0,1,0,0,1],[0,1,1,0,0,1,1],[0,0,0,0,0,1,1],[0,0,0,1,1,0,0],[0,0,1,1,1,0,0]).$

$($a$)$ From the adjacency matrix answer: which node in the network has the highest degree?

$($a$)$

$($b$)$ Calculate the local clustering coefficient for the highest degree node you identified in part