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).
\node[circle, draw]
) are among the basic knowledge you will need. Please help us help you by giving it a try and then posting a minimal code example with which you do need help with.(<angle>:<radius>)
, so for example\node [circle,draw] (m1) at (30:2cm) {$[1]_{m}$};
to place a node at the angle 30 degrees, 2cm from the origin.