Question 6 (Communities)

Consider the following adjacency matrix of an undirected network:

\[ A= \begin{bmatrix} 0&1&1&0&0&0&0\\ 1&0&1&1&0&0&0\\ 1&1&0&1&1&0&0\\ 0&1&1&0&0&1&0\\ 0&0&1&0&0&1&1\\ 0&0&0&1&1&0&1\\ 0&0&0&0&1&1&0 \end{bmatrix} \]

Consider the candidate communities

\[ C_1=\{1,2,3,4\} \qquad C_2=\{5,6,7\} \]

Which statement is correct?

1. \(C_1\) is a clique and \(C_2\) is a strong community
2. \(C_1\) is a strong community but not clique, while \(C_2\) is a clique
3. Both \(C_1\) and \(C_2\) are strong communities but not cliques
4. \(C_1\) is weak only and \(C_2\) is a clique
5. None of the above

Original idea by: Antonio De Cesare Del Nero