\begin{tikzpicture}[scale=0.45]
            % original graph
			\node[circle, draw=black, fill=green, minimum size=10pt] (G1) at (6.0,-4) {};
			\node[circle, draw=black, fill=purple, minimum size=10pt] (P1) at (3.0,-4) {};
			\node[circle, draw=black, fill=cyan, minimum size=10pt] (C1) at (4.5,-5.5) {};
			\node[circle, draw=black, fill=orange, minimum size=10pt] (O1) at (4.5,-2.5) {};
			\node[circle, draw=black, fill=blue, minimum size=10pt] (B1) at (4.5,-4) {};
			\draw[thick] (B1) -- (G1);
			\draw[thick] (G1) -- (O1);
			\draw[thick] (C1) -- (P1);
           	\node[below] at (4.50,-6.00) {\scriptsize Original};	
            
            % rank 1 nodes
			\node[circle, draw=black, fill=green, minimum size=10pt] (G2) at (11.0,-4) {};
			\node[circle, draw=black, fill=purple, minimum size=10pt] (P2) at (8.0,-4) {};
			\node[circle, draw=black, fill=cyan, minimum size=10pt] (C2) at (9.5,-5.5) {};
			\node[circle, draw=black, fill=orange, minimum size=10pt] (O2) at (9.5,-2.5) {};
			\node[circle, draw=black, fill=blue, minimum size=10pt] (B2) at (9.5,-4) {};
			\draw[thick] (B2) -- (G2);
			\draw[thick] (G2) -- (O2);
			\draw[thick] (C2) -- (P2);
			\draw[ultra thick, draw=red] (B2) -- (P2);
			\draw[ultra thick, draw=red] (B2) -- (C2);
			\node[below] at (9.50,-6.00) {\scriptsize Rank $i=1$};	
           
            % rank 2 node
			\node[circle, draw=black, fill=green, minimum size=10pt] (G3) at (16.0,-4) {};
			\node[circle, draw=black, fill=purple, minimum size=10pt] (P3) at (13.0,-4) {};
			\node[circle, draw=black, fill=cyan, minimum size=10pt] (C3) at (14.5,-5.5) {};
			\node[circle, draw=black, fill=orange, minimum size=10pt] (O3) at (14.5,-2.5) {};
			\node[circle, draw=black, fill=blue, minimum size=10pt] (B3) at (14.5,-4) {};
			\draw[thick] (G3) -- (O3);
			\draw[thick] (C3) -- (P3);
			\draw[ultra thick] (B3) -- (P3);
			\draw[ultra thick] (B3) -- (C3);
			\draw[very thick, draw=red] (B3) -- (G3);
			\node[below] at (14.50,-6.00) {\scriptsize Rank $i=2$};	
            
            % rank 3 node
			\node[circle, draw=black, fill=green, minimum size=10pt] (G4) at (21.0,-4) {};
			\node[circle, draw=black, fill=purple, minimum size=10pt] (P4) at (18.0,-4) {};
			\node[circle, draw=black, fill=cyan, minimum size=10pt] (C4) at (19.5,-5.5) {};
			\node[circle, draw=black, fill=orange, minimum size=10pt] (O4) at (19.5,-2.5) {};
			\node[circle, draw=black, fill=blue, minimum size=10pt] (B4) at (19.5,-4) {};
			\draw[thick] (G4) -- (O4);
			\draw[thick] (C4) -- (P4);
			\draw[ultra thick] (B4) -- (P4);
			\draw[ultra thick] (B4) -- (C4);
			\draw[very thick] (B4) -- (G4);
			\draw[thick, draw=red] (B4) -- (O4);
			\node[below] at (19.50,-6.00) {\scriptsize Rank $i=3$};	
			
\end{tikzpicture}
