Gfrktyl

I am trying to draw a Markov chain using tikz. The diagram is in the correct setup except the arrow going from State 2 and 3 overlaps two other arrows. I tried repositioning the states using node distance but that did not seem to work. How can I force the arrows not to overlap?

%latex

documentclass[reqno]{amsart}

usepackage{amsmath}

usepackage{amssymb}

usepackage{hyperref}

usepackage{pgfplots}



usepgfplotslibrary{fillbetween}



usepackage{tikz}

usetikzlibrary{automata}

usetikzlibrary{positioning}  %                 ...positioning nodes

usetikzlibrary{arrows}       %                 ...customizing arrows

tikzset{node distance=4.5cm, % Minimum distance between two nodes. Change if necessary.

         every state/.style={ % Sets the properties for each state

           semithick,

           fill=gray!10},

         initial text={},     % No label on start arrow

         double distance=4pt, % Adjust appearance of accept states

         every edge/.style={  % Sets the properties for each transition

         draw,

           ->,>=stealth',     % Makes edges directed with bold arrowheads

           auto,

           semithick}}



begin{document}



begin{figure}[htb]

centering

begin{tikzpicture}

node[state] (s1) {State 1};

node[state, below right of=s1] (s2) {State 2};

node[state, below left of=s1] (s3) {State 3};



draw (s1) edge[loop above] node {} (s1);

draw (s1) edge[bend left] node {} (s2);

draw (s1) edge[bend right] node {} (s3);



draw (s2) edge[bend left] node {} (s1);

draw (s2) edge[loop right] node {} (s2);

draw (s2) edge[bend right] node {} (s3);



draw (s3) edge[bend right] node {} (s1);

draw (s3) edge[bend right] node {} (s2);

draw (s3) edge[loop left] node {} (s3);



end{tikzpicture}

end{figure}



end{document}

bend left and bend right come with parameters, the bending angles. Adjusting them allows you to avoid the intersections. (BTW, I also removed packages that were not used. Note also that the arrows library got superseded by arrows.meta but I kept arrows for now.)

documentclass[reqno]{amsart}

usepackage{tikz}

usetikzlibrary{automata}

usetikzlibrary{positioning}  %                 ...positioning nodes

usetikzlibrary{arrows}       %                 ...customizing arrows

tikzset{node distance=4.5cm, % Minimum distance between two nodes. Change if necessary.

         every state/.style={ % Sets the properties for each state

           semithick,

           fill=gray!10},

         initial text={},     % No label on start arrow

         double distance=4pt, % Adjust appearance of accept states

         every edge/.style={  % Sets the properties for each transition

         draw,

           ->,>=stealth',     % Makes edges directed with bold arrowheads

           auto,

           semithick}}



begin{document}



begin{figure}[htb]

centering

begin{tikzpicture}

node[state] (s1) {State 1};

node[state, below right of=s1] (s2) {State 2};

node[state, below left of=s1] (s3) {State 3};



draw (s1) edge[loop above]  (s1);

draw (s1) edge[bend left]  (s2);

draw (s1) edge[bend right]  (s3);



draw (s2) edge[bend left=12]  (s1);

draw (s2) edge[loop right]  (s2);

draw (s2) edge[bend right=12]  (s3);



draw (s3) edge[bend right=12]  (s1);

draw (s3) edge[bend right]  (s2);

draw (s3) edge[loop left]  (s3);



end{tikzpicture}

end{figure}

end{document}

you can reduce default value of bend angle. just add bend angle=15 to your tikzset (similarly @marmoth change it locally for two arrows bend).

off topic:

• for labeling of arrows is handy to use quotes library and than wrote it as for example ... (s1) edge["label",bend left] (s2).


• 
  

  package hyperref had to be load last in preamble (except in rare exception)

  
  
  

  documentclass[reqno]{amsart}
  
  usepackage{amsmath, amssymb}
  
  
  
  usepackage{pgfplots}         % it load tikz too
  
  pgfplotsset{compat=1.16}
  
  usetikzlibrary{automata,
  
                  arrows.meta,    %   ...customizing arrows
  
                  positioning,    %   ...positioning nodes
  
                  quotes}         % For edge labels
  
  usepgfplotslibrary{fillbetween}
  
  tikzset{node distance=4.5cm,   % Minimum distance between nodes. Change if necessary.
  
           every state/.style={   % Sets the properties for each state
  
                  semithick,
  
                  fill=gray!10},
  
           initial text={},       % No label on start arrow
  
           double distance=4pt,   % Adjust appearance of accept states
  
           every edge/.style={    % Sets the properties for each transition
  
                  draw,
  
                  semithick,
  
                  -Stealth,       % Makes edges directed with bold arrowheads
  
                  auto},
  
           bend angle=15          % Reduce default bend angle
  
           }
  
  
  
  usepackage{hyperref}           % had to be last in preamble
  
  
  
  begin{document}
  
      begin{figure}[htb]
  
      centering
  
  begin{tikzpicture}
  
  node[state] (s1) {State 1};
  
  node[state, below right of=s1] (s2) {State 2};
  
  node[state, below left of=s1] (s3) {State 3};
  
  
  
  draw   (s1) edge[loop above]   (s1)
  
          (s1) edge[bend left]    (s2)
  
          (s1) edge[bend right]   (s3)
  
  %
  
          (s2) edge[bend left]    (s1)
  
          (s2) edge[loop right]   (s2)
  
          (s2) edge[bend right]   (s3)
  
  %
  
          (s3) edge[bend right]   (s1)
  
          (s3) edge[bend right]   (s2)
  
          (s3) edge[loop left]    (s3);
  
  end{tikzpicture}
  
      end{figure}
  
  end{document}