How to change the position of weights of nodes in a digraph

Question

I used the following latex code to draw this digraph.

\documentclass[12pt]{article}
\usepackage{pgf, tikz}
\usetikzlibrary{arrows, automata}
\begin{document}
\begin{tikzpicture}
       [> = stealth,
        shorten > = 1pt, 
        auto,
        node distance = 2cm, 
        thick ]

    \tikzstyle{every state}=[
        draw = black,
        thick,
        fill = white,
        minimum size = 2mm]

    \node[state] (v1) {$v_1$};
     \node[state] (v2) [right of=v1] {$v_2$};
       \path[->] (v2) edge node {$1$} (v1);
      \node[state] (v3) [right of=v2] {$v_3$};
        \path[->] (v3) edge node {$1$} (v2);
      \node[state] (v4) [right of=v3] {$v_4$};
       \path[->] (v4) edge node {$1$} (v3);
     \node[state] (v5) [right of=v4] {$v_5$};
       \path[->] (v5) edge node {$1$} (v4);
     \node[state] (v6) [right of=v5] {$v_6$};
       \path[->] (v6) edge node {$1$} (v5);

         \path (v1) edge [loop left] node {$u_1$} (v1);
        \path[->] (v1) edge[bend left=30] node {$u_2$}  (v2);
         \path[->] (v1) edge[bend left=40] node  {$u_3$}  (v3);
          \path[->] (v1) edge[bend left=50] node {$u_4$}  (v4);
           \path[->] (v1) edge[bend left=55] node {$u_5$}  (v5);
            \path[->] (v1) edge[bend left=60] node  {$u_6$}  (v6);

   \end{tikzpicture}
   \end{document}

I would greatly appreciate to improve my latex code such that the output of code be similar to the mentioned digraph. In fact my problems are the size of circles that want to be smaller and the positions of $u_i$’s and the loop for the node v_1.

Thanks for any suggestion.

Answer 1

I like to use the quotes library to make edge labels, because it offers the syntax (source) edge["label"] (target) which is shorter than (source) edge node {label} (target). The option to control the position of the label is pos; I think pos=0.8 leads to reasonable output, but you could fiddle with it yourself. I also used a \foreach loop to simplify your first bit of code.

\documentclass[12pt]{article}
\usepackage{pgf, tikz}
\usetikzlibrary{arrows, automata,quotes} % quotes library adds quotes syntax
\begin{document}
\begin{tikzpicture}
       [> = stealth,
        shorten > = 1pt, 
        auto,
        node distance = 2cm, 
        thick , 
        % automatically put nodes in math mode:
        execute at begin node=$,execute at end node=$ 
]

    \tikzset{every state/.style={thick,minimum size = 2mm}}

  \node[state] (v1) {v_1};  
    % Use a loop to make the states. \lastn holds \n minus 1 
  \foreach \n[remember=\n as \lastn (initially 1)] in {2,...,6}{
         \node[state] (v\n) [right of=v\lastn] {v_\n};
         \draw[<-] (v\lastn) edge["1"'] (v\n);
    }


        \draw (v1) edge [loop left,"u_1"]  (v1);
  % Put all the rest of the labels 8/10ths of the way across the edge
    \tikzset{every edge quotes/.style={pos=0.8}}
        \draw[->] (v1) edge[bend left=30,"u_2" ] (v2);
        \draw[->] (v1) edge[bend left=40,"u_3"]  (v3);
        \draw[->] (v1) edge[bend left=50,"u_4"]  (v4);
        \draw[->] (v1) edge[bend left=55,"u_5"]  (v5);
        \draw[->] (v1) edge[bend left=60,"u_6"] (v6);

   \end{tikzpicture}
   \end{document}

Answer 2

slightly modified nice Hood Chatham's answer (most changes are off-topic):

\documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{arrows, automata, quotes} 

\begin{document}
\begin{tikzpicture}
       [shorten > = 1pt,
        auto,
        node distance = 2cm,
        thick ,
        execute at begin node=$,execute at end node=$,% put nodes in math mode ...
    every state/.style = {thick, minimum size=4mm, inner sep=1mm},  % <--- added
    every  edge/.style = {draw, -stealth},                          % <--- added 
        ]
  \node[state] (v1) {v_1};
  % Use a loop to make the states. \lastn holds \n minus 1
  \foreach \n [remember=\n as \lastn (initially 1)] in {2,...,6}%
  {
    \node[state] (v\n) [right of=v\lastn] {v_\n};
    \draw (v\n) edge["1"] (v\lastn);                                % <--- changed
  }
  \draw (v1) edge [out=135, in=225, looseness=8, "u_1" ']  (v1);    % <--- added
  % bended edges
  \foreach \i [evaluate=\i as \a using 30 + 6*\i] in {2,...,6}      % <--- added
  \draw (v1) edge[inner sep=1pt, pos=0.75, bend left=\a, "u_\i"]    (v\i);  % <--- modified
   \end{tikzpicture}
   \end{document}

addendum:

if i correctly understood your comment, you like change the first solution to something like this:

in mwe below are changes in comparison of above mwe indicated with % <--- new:

\documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{arrows, automata, 
                chains,                                             % <--- new
                positioning,                                        % <--- new
                quotes} 

\begin{document}
\begin{tikzpicture}
       [shorten > = 1pt,
        auto,
        node distance = 2cm,
        start chain = grow right,                                   % <--- new
        thick ,
        execute at begin node=$,execute at end node=$,% put nodes in math mode ...
    every state/.style = {thick, minimum size=4mm, inner sep=1mm,
                          on chain},                                % <--- new
    every  edge/.style = {draw, -stealth},                          
        ]
  \foreach \i [count=\j from 1] in {1,2,3,n}                        % <--- changed
    \node (v\j) [state, on chain] {v_\i};                           % <--- changed
  \foreach \i [count=\j from 1] in {2,...,4}                        % <--- new
  {
    \ifnum\i<4                                                      % <--- new
    \draw (v\i) edge["1"] (v\j);                                    % <--- new
    \else                                                           % <--- new
    \draw[-, very thick, dotted,                                    % <--- new
          shorten <=1mm] (v\i) -- (v\j);                            % <--- new
    \fi                                                             % <--- new
  }
  % bended edges
  \foreach \i [count=\j from 2,                                     % <--- new
               evaluate=\j as \a using 30 + 6*\j] in {2,3,n}        % <--- changed
  \draw (v1) edge[inner sep=1pt, pos=0.75, bend left=\a, "u_\i"]    (v\j);  
  \draw (v1) edge [out=135, in=225, looseness=8, "u_1" ']  (v1);    
\end{tikzpicture}
\end{document}