Creating combinations of a graph using loops

Question

In the blue graph at the left there are 5 connections. From this graph one can create sub-graphs using for instance 3 of the connections. There would be a total of 10 combinations.

Is there a smart way to create and draw these combinations? Probably by using \foreach.

\documentclass[border=5pt]{standalone}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}

\usepackage{tikz}
\usetikzlibrary{positioning,matrix,shapes,arrows,calc}




\begin{document}

                \begin{tikzpicture}[>=stealth',auto,node distance=2cm,
                  thick,main node/.style={circle,draw,font=\sffamily\Large\bfseries},dashnode/.style={circle,draw,dashed,font=\sffamily\Large\bfseries}]
                  
                  
                  
                    \node[main node,blue] at (0, 0)   (1) {1};
                    \node[main node,blue] at (1, 1)  (2) {2};
                    \node[main node,blue] at (1, -1)  (3) {3};
                    \node[main node,blue] at (2, 0)  (4) {4};
                
                    \draw [blue] (1) -- (2);
                    \draw [blue] (1) -- (3);
                    \draw [blue] (2) -- (4);
                    \draw [blue] (2) -- (3);
                    \draw [blue] (3) -- (4);

                    \node[main node] at (3, 0)   (1) {1};
                    \node[main node] at (4, 1)  (2) {2};
                    \node[main node] at (4, -1)   (3) {3};
                    \node[main node] at (5, 0)   (4) {4};
                

                    \foreach \k in {(1) -- (2),(2) -- (3),(2) -- (4)} {
                      \draw \k ;
                    }
                    
                    \node[main node] at (6, 0)   (1) {1};
                    \node[main node] at (7, 1)  (2) {2};
                    \node[main node] at (7, -1)   (3) {3};
                    \node[main node] at (8, 0)   (4) {4};

                    \foreach \k in {(1) -- (3),(2) -- (3),(3) -- (4)} {
                      \draw \k ;
                    }
                \end{tikzpicture}
                
                

\end{document}

EDIT

After the very helpful comments from @Excelsior the problem has been codes as:

\documentclass[border=5pt]{standalone}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}

\usepackage{tikz}
\usetikzlibrary{positioning,matrix,shapes,arrows,calc}

\begin{document}

                % \begin{tikzpicture}[>=stealth',auto,node distance=2cm,
                %   thick,main node/.style={circle,draw,font=\sffamily\Large\bfseries},dashnode/.style={circle,draw,dashed,font=\sffamily\Large\bfseries}]
                  
                  
                  
                %     \node[main node,blue] at (0, 0)   (1) {1};
                %     \node[main node,blue] at (1, 1)  (2) {2};
                %     \node[main node,blue] at (1, -1)  (3) {3};
                %     \node[main node,blue] at (2, 0)  (4) {4};
                
                %     \draw [blue] (1) -- (2);
                %     \draw [blue] (1) -- (3);
                %     \draw [blue] (2) -- (4);
                %     \draw [blue] (2) -- (3);
                %     \draw [blue] (3) -- (4);

                %     \node[main node] at (3, 0)   (1) {1};
                %     \node[main node] at (4, 1)  (2) {2};
                %     \node[main node] at (4, -1)   (3) {3};
                %     \node[main node] at (5, 0)   (4) {4};
                

                %     \foreach \k in {(1) -- (2),(2) -- (3),(2) -- (4)} {
                %       \draw \k ;
                %     }
                    
                %     \node[main node] at (6, 0)   (1) {1};
                %     \node[main node] at (7, 1)  (2) {2};
                %     \node[main node] at (7, -1)   (3) {3};
                %     \node[main node] at (8, 0)   (4) {4};

                %     \foreach \k in {(1) -- (3),(2) -- (3),(3) -- (4)} {
                %       \draw \k ;
                %     }

                % \end{tikzpicture}
                
                \begin{tikzpicture}[
        >=stealth', auto, node distance=2cm, thick, 
        main node/.style={circle, draw, font=\sffamily\Large\bfseries}, dashnode/.style={circle,draw,dashed,font=\sffamily\Large\bfseries}]     
        
        \node[main node,blue] at (0, 0) (1-0) {1};
        \node[main node,blue] at (1, 1) (2-0) {2};
        \node[main node,blue] at (1,-1) (3-0) {3};
        \node[main node,blue] at (2, 0) (4-0) {4};
        
        \draw [blue] (1-0) -- (2-0);
        \draw [blue] (1-0) -- (3-0);
        \draw [blue] (2-0) -- (4-0);
        \draw [blue] (2-0) -- (3-0);
        \draw [blue] (3-0) -- (4-0);
        
        \foreach [evaluate=\i as \x using {3*(\i)}] \i in {1,...,11} {
            \foreach \n in {1,...,4}{
                \node[main node] at ($ (\n-0) + (\x,0) $) (\n-\i) {\n};
            }
        }
        
        % node system 1

        \foreach \k in {(1-1) -- (2-1),
                        (2-1) -- (3-1),
                        (2-1) -- (4-1)} {
            \draw \k ;
        }
        
        % node system 2
        \draw (1-2) -- (2-2);
        \draw (2-2) -- (3-2);
        \draw (3-2) -- (4-2);
    \end{tikzpicture}

\end{document}

With the following result:

Answer 1

I tried to draw 10 additional node systems and labeled them according to their number. You may know best the possible combinations, so I leave them empty.

\documentclass[border=5pt]{standalone}

\usepackage{tikz}
\usetikzlibrary{positioning,matrix,shapes,arrows,calc}

\begin{document}
    
    \begin{tikzpicture}[
        >=stealth', auto, node distance=2cm, thick, 
        main node/.style={circle, draw, font=\sffamily\Large\bfseries}, dashnode/.style={circle,draw,dashed,font=\sffamily\Large\bfseries}]     
        
        \node[main node,blue] at (0, 0) (1-0) {1};
        \node[main node,blue] at (1, 1) (2-0) {2};
        \node[main node,blue] at (1,-1) (3-0) {3};
        \node[main node,blue] at (2, 0) (4-0) {4};
        
        \draw [blue] (1-0) -- (2-0);
        \draw [blue] (1-0) -- (3-0);
        \draw [blue] (2-0) -- (4-0);
        \draw [blue] (2-0) -- (3-0);
        \draw [blue] (3-0) -- (4-0);
        
        \foreach [evaluate=\i as \x using {3*(\i)}] \i in {1,...,11} {
            \foreach \n in {1,...,4}{
                \node[main node] at ($ (\n-0) + (\x,0) $) (\n-\i) {\n};
            }
        }
        
        % node system 1
        \draw (1-1) -- (2-1);
        \draw (2-1) -- (3-1);
        \draw (2-1) -- (4-1);
        
        % node system 2
        \draw (1-2) -- (2-2);
        \draw (2-2) -- (3-2);
        \draw (3-2) -- (4-2);
    \end{tikzpicture}
\end{document}

If you need more node systems, you just have to increase the maximum of \i.

EDIT

The possible combination were added:

\documentclass[border=5pt]{standalone}

\usepackage{tikz}
\usetikzlibrary{positioning,matrix,shapes,arrows,calc}

\begin{document}
    
    \begin{tikzpicture}[
        >=stealth', auto, node distance=2cm, thick, 
        main node/.style={circle, draw, font=\sffamily\Large\bfseries}, dashnode/.style={circle,draw,dashed,font=\sffamily\Large\bfseries}]     
        
        \node[main node,blue] at (0, 0) (1-0) {1};
        \node[main node,blue] at (1, 1) (2-0) {2};
        \node[main node,blue] at (1,-1) (3-0) {3};
        \node[main node,blue] at (2, 0) (4-0) {4};
        
        \draw [blue] (1-0) -- (2-0);
        \draw [blue] (1-0) -- (3-0);
        \draw [blue] (2-0) -- (4-0);
        \draw [blue] (2-0) -- (3-0);
        \draw [blue] (3-0) -- (4-0);
        
        \foreach [evaluate=\i as \x using {3*(\i)}] \i in {1,...,10} {
            \foreach \n in {1,...,4}{
                \node[main node] at ($ (\n-0) + (\x,0) $) (\n-\i) {\n};
            }
        }
        
        % node system 1
        \draw (1-1) -- (2-1);
        \draw (2-1) -- (4-1);
        \draw (2-1) -- (3-1);
        
        % node system 2
        \draw (1-2) -- (2-2);
        \draw (2-2) -- (4-2);
        \draw (1-2) -- (3-2);
        
        % node system 3
        \draw (1-3) -- (2-3);
        \draw (2-3) -- (4-3);
        \draw (3-3) -- (4-3);
        
        % node system 4
        \draw (1-4) -- (2-4);
        \draw (2-4) -- (3-4);
        \draw (1-4) -- (3-4);
        
        % node system 5
        \draw (1-5) -- (2-5);
        \draw (2-5) -- (3-5);
        \draw (3-5) -- (4-5);
        
        % node system 6
        \draw (1-6) -- (2-6);
        \draw (1-6) -- (3-6);
        \draw (3-6) -- (4-6);
        
        % node system 7
        \draw (1-7) -- (3-7);
        \draw (2-7) -- (3-7);
        \draw (3-7) -- (4-7);
        
        % node system 8
        \draw (2-8) -- (4-8);
        \draw (2-8) -- (3-8);
        \draw (3-8) -- (4-8);
        
        % node system 9
        \draw (2-9) -- (4-9);
        \draw (2-9) -- (3-9);
        \draw (1-9) -- (3-9);
        
        % node system 10
        \draw (2-10) -- (4-10);
        \draw (3-10) -- (4-10);
        \draw (1-10) -- (3-10);
    \end{tikzpicture}
\end{document}