Getting vdots in graph tree

Question

\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{tikz}
\tikzstyle{vertex}=[auto=left,circle,fill=black!25,minimum size=20pt,inner sep=0pt]

\begin{document}    

\begin{tikzpicture}
      \node[vertex] (n1)  at (1,4)  {s};
      \node[vertex] (n2)  at (3,2)  {};
      \node[vertex] (n3)  at (3,3)  {};
      \node[vertex] (n4)  at (3,4)  {};
      \node[vertex] (n5)  at (3,6)  {};
      \node[vertex] (n6)  at (9,4)  {t};
      \node[vertex] (n7)  at (7,6)  {};
      \node[vertex] (n8)  at (7,4)  {};
      \node[vertex] (n9)  at (7,3)  {};
      \node[vertex] (n10) at (7,2)  {};

      \foreach \from/\to in {n1/n2,n1/n3,n1/n4,n1/n5,
                n6/n7,n6/n8,n6/n9,n6/n10}
      \draw[densely dotted] (\from) -- (\to);
      \foreach \from/\to in {n2/n10,n3/n9,n4/n8,n5/n7}
      \draw(\from) -- (\to);
      \end{tikzpicture}

\end{document}

I am trying to get vertical dots between nodes (n4,n5) and (n6,n7). I have tried many ways but nonetheless.

Also I am trying t add edge weights to the graph. I keep finding links to those written in the form of a matrix.

I need to add text representing the left and right nodes on the tree. How do we add text at desired place in the tree?

Answer 1

1. To place any character, such as \dots, you can use a \path and place the required character via a node and use the sloped option so that the character is rotated along the path:

   \path (n4) -- (n5) node [red, font=\Huge, midway, sloped] {$\dots$};
   \path (n6) -- (n7) node [red, font=\Huge, midway, sloped] {$\dots$};
   

   If you are not satisfied with these, you could add small filled circles.

2. The nodes at the start and end can be added and positions via a left/right option so the text is placed to the left/right of the specfic point of the node:

    \node [left ] at (n1.west) {start};
    \node [right] at (n6.east) {end};
   

3. To add text above each edge you can add another option to the \foreach loop and place the text via a node:

   node [midway, above, orange] {$\weight$}
   

   

Code:

\documentclass[border=2pt]{standalone}
\usepackage{tikz}

\tikzstyle{vertex}=[auto=left,circle,fill=black!25,minimum size=20pt,inner sep=0pt]

\begin{document}
\begin{tikzpicture}
  \node[vertex] (n1)  at (1,4)  {s};
  \node[vertex] (n2)  at (3,2)  {$n_2$};
  \node[vertex] (n3)  at (3,3)  {$n_3$};
  \node[vertex] (n4)  at (3,4)  {$n_4$};
  \node[vertex] (n5)  at (3,6)  {$n_5$};
  \node[vertex] (n6)  at (9,4)  {t};
  \node[vertex] (n7)  at (7,6)  {$n_7$};
  \node[vertex] (n8)  at (7,4)  {$n_8$};
  \node[vertex] (n9)  at (7,3)  {$n_9$};
  \node[vertex] (n10) at (7,2)  {$n_{10}$};

  \foreach \from/\to/\weight in {n1/n2/a, n1/n3/b, n1/n4/c, n1/n5/d,
            n6/n7/e, n6/n8/f, n6/n9/g, n6/n10/h}
  \draw[densely dotted] (\from) -- (\to) node [midway, above, orange] {$\weight$};
  \foreach \from/\to/\weight in {n2/n10/i, n3/n9/j, n4/n8/k, n5/n7/l}
  \draw(\from) -- (\to) node [midway, above, orange] {$\weight$};;

  % These are for dotted lines
  %\draw [red, dotted, ultra thick] (n4) -- (n5);
  %\draw [blue,dotted, ultra thick] (n6) -- (n7);

  \path (n4) -- (n5) node [red, font=\Huge, midway, sloped] {$\dots$};
  \path (n6) -- (n7) node [red, font=\Huge, midway, sloped] {$\dots$};

  \node [left , red] at (n1.west) {start};
  \node [right, red] at (n6.east) {end};
\end{tikzpicture}
\end{document}