Unable to add edges to a graph

Question

\begin{figure}[H]
        \centering
        
        \begin{tikzpicture}[
        C/.style = {circle, draw}, %   C: circle
        every edge quotes/.style = {auto, font=\footnotesize, inner sep=2pt, pos=0.8}
        ]
        \begin{scope}[nodes={C}]
        \node (a1)   at (0,0)        {$v_2$};
        \node (a3) at (5,0)  {$v_4$};
        \node (a2) at (3,1) {$v_3$};
        \node (a0) at (2,-2)  {$v_1$};
        \node (a4) at (3,-1)  {$v_5$};
        \node (a6) at (2,2)  {$v_6$};
        \end{scope}
        %
        \path 
        (a1) edge ["\hspace{40mm} $e_{23}$"]  (a2)
        (a1) edge ["$e_{24}$"]  (a3)
        (a1) edge ["$e_{25}$"]  (a4)
        (a1) edge ["$e_{26}$"]  (a6)
        (a1) edge ["$e_{21}$"]  (a0);
        
    \end{tikzpicture}
\end{figure}

Why cant I add edges between the vertices $3$ and $4$ in this tikz picture? I dont know why when I add an edge between vertices $v_3$ and $v_4$ with a edge label $e_{34}$, the new edge does not show up and the entire graph gets disturbed.

Where am I doing wrong here? Can someone please help me out here.

Answer 1

In general, in order to label edges you essentially need to place a node along the path of the edge. Whithout loading any TikZ library, this can be done as follows:

\documentclass[tikz,border=1pt]{standalone}

\begin{document}

    \begin{tikzpicture}[
    C/.style = {circle, draw}, %   C: circle
    every edge quotes/.style = {auto, font=\footnotesize, inner sep=2pt, pos=0.8}
    ]
    
    \begin{scope}[nodes={C}]
    \node (a1) at (0,0)  {$v_2$};
    \node (a3) at (5,0)  {$v_4$};
    \node (a2) at (3,1)  {$v_3$};
    \node (a0) at (2,-2) {$v_1$};
    \node (a4) at (3,-1) {$v_5$};
    \node (a6) at (2,2)  {$v_6$};
    \end{scope}
    
    \path 
    (a1) edge node {\hspace{40mm} $e_{23}$} (a2)
    (a1) edge node[below, pos=.75] {$e_{24}$} (a3)
    (a1) edge node[below] {$e_{25}$} (a4)
    (a1) edge node[below, xshift=5pt] {$e_{26}$} (a6)
    (a1) edge node[below, yshift=-3pt] {$e_{21}$} (a0);
    
    \end{tikzpicture}

\end{document}

You can use the options above or below to place the label node above or below the edge. It is placed midways between the start and end point of the edge by default, but you can use the pos option to shift it (where pos=0 means at the start point and pos=1 at the end point). You may want to additionally shift the labels using xshift and yshift.

However, you probably got your code from someone who used the TikZ library quotes. You need to load this library in your preamble if you want to use it:

\documentclass[tikz,border=1pt]{standalone}

\usetikzlibrary{quotes} % <-- add this!

\begin{document}

    \begin{tikzpicture}[
        C/.style = {circle, draw}, %   C: circle
        every edge quotes/.style = {auto, font=\footnotesize, inner sep=2pt, pos=0.8}
        ]
        \begin{scope}[nodes={C}]
        \node (a1)   at (0,0)        {$v_2$};
        \node (a3) at (5,0)  {$v_4$};
        \node (a2) at (3,1) {$v_3$};
        \node (a0) at (2,-2)  {$v_1$};
        \node (a4) at (3,-1)  {$v_5$};
        \node (a6) at (2,2)  {$v_6$};
        \end{scope}
        %
        \path 
        (a1) edge ["$e_{23}$"{xshift=5pt}]  (a2)
        (a1) edge ["$e_{24}$"]  (a3)
        (a1) edge ["$e_{25}$"]  (a4)
        (a1) edge ["$e_{26}$"]  (a6)
        (a1) edge ["$e_{21}$"]  (a0);
        
    \end{tikzpicture}

\end{document}

You can still use the above mentioned options to shift the node. See the example fot the edge between nodes (a1) and (a2) in the above example.