How to draw the following diagram using tikz?

Question

I am trying to draw the following cyclic birth and death chain using tikz:

The key elements I require are:

1. Labels inside the circles
2. Arrowheads in middle of arrows
3. Ellipses at bottom of diagram
4. Arrows going in both directions at each node.

I found a very similar one over here: Drawing cyclic quiver , but it lacked arrows going both directions and labels within nodes.

I have drawn this related diagram already:

Any help would be greatly appreciated (and explanation of code would also be really helpful!)

Thanks!! :)

Answer 1

This is how I would do it, but since you gave no MWE (not even of the diagram you already made) I don't know if it is of use to you.

\documentclass[tikz]{standalone}

\usetikzlibrary{decorations.markings}

\tikzset{state/.style={draw,circle,minimum size=1.75cm}}

\begin{document}
    \begin{tikzpicture}
        \node[state] (0)   at ( 90:4) {\( [0]_m \)};
        \node[state] (1)   at ( 45:4) {\( [1]_m \)};
        \node[state] (2)   at (  0:4) {\( [2]_m \)};
        \node[state] (i)   at (270:4) {\( [i]_m \)};
        \node[state] (m-2) at (180:4) {\( [m-2]_m \)};
        \node[state] (m-1) at (135:4) {\( [m-1]_m \)};

        \node[state,draw=none,rotate=315+90] (i-1) at (315:4) {\( \cdots \)};
        \node[state,draw=none,rotate=225+90] (i+1) at (225:4) {\( \cdots \)};

        \begin{scope}[decoration={markings,mark=at position 0.6 with {\arrow{latex}}},every node/.style={auto,font=\small}]
            \foreach \startnode/\endnode in {0/1,1/2,2/i-1,i-1/i,i/i+1,i+1/m-2,m-2/m-1,m-1/0}{
                \draw[postaction={decorate}] (\startnode) to[bend left=25] node[auto] {\( P_{\startnode} \)} (\endnode);
                \draw[postaction={decorate}] (\endnode)   to[bend left=25] node[auto] {\( 1-P_{\endnode} \)} (\startnode);
            }
        \end{scope}
    \end{tikzpicture}
\end{document}

The result looks like this:

Note that Tikz also has the automata library which may be better suited for this type of diagrams. See page 513 of the PGF manual (v3.0.1a).