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How to use the tikz package to achieve the following. I looked at but still couldn't get it done. Any help is much appreciated.

There are many possible ways to draw this, here is one of them.

documentclass[tikz,border=3.14mm]{standalone}

usetikzlibrary{matrix,backgrounds}

begin{document}

begin{tikzpicture}

matrix[matrix of nodes,nodes={circle,draw,fill=white},column sep=3mm,row sep=3mm] (mat) { 2 & 7 & 6 \

9 & 5 & 1\

4 & 3 & 8\

};

foreach X in {1,2,3}

{foreach Y [evaluate=Y as Z using {int(10*X+Y)}]in {1,2,3}

{ifnumZ=22

else

draw (mat-X-Y) -- (mat-2-2);

fi}}

begin{scope}[on background layer]

 draw (mat-3-1) rectangle (mat-1-3);

end{scope}

end{tikzpicture}

end{document}

Alternatively, if you do not want to fill the nodes, you could use

documentclass[tikz,border=3.14mm]{standalone}

usetikzlibrary{matrix}

begin{document}

begin{tikzpicture}

matrix[matrix of nodes,nodes={circle,draw},column sep=3mm,row sep=3mm] (mat) { 2 & 7 & 6 \

9 & 5 & 1\

4 & 3 & 8\

};

foreach X [count=XX starting from 0] in {1,2,3}

{foreach Y [evaluate=Y as Z using {int(10*X+Y)},count=YY starting from 0]in {1,2,3}

{ifnumZ=22

else

draw (mat-X-Y) -- (mat-2-2);

fi

ifnumX=1

else

draw (mat-XX-Y) -- (mat-X-Y);

fi

ifnumY=1

else

draw (mat-X-YY) -- (mat-X-Y);

fi

}}

end{tikzpicture}

end{document}