$\begin{array}{|c|c|c|c|c|c|c|} \hline 0 & 1 & 1 & 0 & 1 & 1 & 0 \\ \hline 1 & 0 & 0 & 1 & 1 & 0 & 1 \\ \hline 1& 0 & 0 & 1 & 1 & 1 & 0 \\ \hline 0 & 1 & 1 & 0 & 1 & 0 & 1 \\ \hline 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ \hline 1 & 0 & 1 & 0 & 0 & 0 & 1 \\ \hline 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ \hline \end{array}$
Consider the above given adjacency matrix representation of a graph containing $7$ nodes (namely A , B, C, D, E, F, G). The Chromatic number of the given graph is?