How to plot the following diagram using TikZ?

Question

I want to draw the following figure in LaTeX using TikZ. How to I do that?

I tried with the code given below but there are still some errors.

Package pgfkeys Error: I do not know the key '/tikz/\protect \OT1\textellipsis ' and I am going to ignore it. Perhaps you misspelled it. \node[dotnode]

Extra \endcsname. \node[dotnode]

Missing \endcsname inserted. \node[dotnode]

How do I get rid of these errors and can the code be shortened further?

\documentclass{article}
\usepackage[margin=2cm]{geometry}
\usepackage{tikz}
\usetikzlibrary{shapes,arrows.meta}
\tikzstyle{mynode}=[ellipse,draw,inner xsep=.2cm,inner ysep=.1cm]
\tikzstyle{dotnode}=[\dots]
\tikzstyle{toparrow}=[->,transform canvas={yshift=4pt}]
\tikzstyle{bottomarrow}=[->,transform canvas={yshift=-4pt}]

\begin{document}

\begin{tikzpicture}[line width=1pt,>={Straight   Barb[length=4pt,width=4pt]},shorten >=3pt,shorten <=3pt]
\node[mynode] (00) at (0,0) {$0,\color{blue}{0}$};
\node[mynode] (10) at (2.5,0) {$1,\color{blue}{0}$};
\node[mynode] (20) at (5,0) {$2,\color{blue}{0}$};
\node[dotnode] (30) at (7.5,0) {$\dots$};
\node[mynode] (40) at (10,0) {\tiny$ L_e(1),\color{blue}{0}$};
\node[mynode] (50) at (13.5,0) {\tiny $L_e(1)+1,\color{blue}{0}$};
\draw[toparrow] (00) to node[above] {$\lambda$} (10);
\draw[bottomarrow] (10) to node[below] {$\eta$} (00);
\draw[toparrow] (10) to node[above] {$\lambda$} (20);
\draw[bottomarrow] (20) to node[below] {$\eta$} (10);
\draw[toparrow] (20) to node[above] {$\lambda$} (30);
\draw[bottomarrow] (30) to node[below] {$\eta$} (20);
\draw[toparrow] (30) to node[above] {$\lambda$} (40);
\draw[bottomarrow] (40) to node[below] {$\eta$} (30);
\draw[toparrow] (40) to node[above] {$\lambda$} (50);
\draw[bottomarrow] (50) to node[below] {$\eta$} (40);
%
\node[mynode] (11) at (2.5,2) {$1,\color{red}{2}$};
\node[mynode] (21) at (5,2) {$2,\color{red}{2}$};
\node[dotnode] (31) at (7.5,2) {$\dots$};
\node[mynode] (41) at (10,2) {\tiny$ L_e(1), \color{red}{2}$};
\node[mynode] (51) at (13.5,2) {\tiny$ L_e(1)+1,\color{red}{2}$};
\node[mynode] (61) at (16.5,2) {\tiny$ L_e(1)+2,\color{red}{2}$};
\draw[toparrow] (11) to node[above] {$\lambda$} (21);
\draw[bottomarrow] (21) to node[below] {$\mu$} (11);
\draw[toparrow] (21) to node[above] {$\lambda$} (31);
\draw[bottomarrow] (31) to node[below] {$\mu$} (21);
\draw[toparrow] (31) to node[above] {$\lambda$} (41);
\draw[bottomarrow] (41) to node[below] {$\mu$} (31);
\draw[toparrow] (41) to node[above] {$\lambda$} (51);
\draw[bottomarrow] (51) to node[below] {$\mu$} (41);
\draw[toparrow] (51) to node[above] {$\lambda$} (61);
\draw[bottomarrow] (61) to node[below] {$\mu$} (51);
%
\node[mynode] (02) at (0,4) {$0,\color{blue}{0}$};
\node[mynode] (12) at (2.5,4) {$1,\color{blue}{0}$};
\node[mynode] (22) at (5,4) {$0,\color{blue}{0}$};
\node[dotnode] (32) at (7.5,4) {$\dots$};
\node[mynode] (42) at (10,4) {\tiny$ L_e(1),\color{blue}{0}$};
\node[mynode] (52) at (13.5,4) {\tiny$ L_e(1)+1,\color{blue}{0}$};
\draw[toparrow] (02) to node[above] {$\lambda$} (12);
\draw[toparrow] (12) to node[above] {$\lambda$} (22);
\draw[toparrow] (22) to node[above] {$\lambda$} (32);
\draw[toparrow] (32) to node[above] {$\lambda$} (42);
\draw[toparrow] (42) to node[above] {$\lambda$} (52);
\draw[->] (12) to node[right] {$\theta$} (11);
\draw[->] (22) to node[right] {$\theta$} (21);
\draw[->] (52) to node[right] {$\theta$} (51);
\draw[->] (42) to node[right] {$\theta$} (41);
%
\draw[->] (10) to node[right] {$\phi$} (11);
\draw[->] (20) to node[right] {$\phi$} (21);
\draw[->] (40) to node[right] {$\phi$} (41);
\draw[->] (50) to node[right] {$\phi$} (51);
\draw[->,draw=green] (11) to node[auto,swap] {$\bar p \mu$} (00);
\draw[->,draw=green] (11) to node[auto,swap] {$p \mu$} (02);
%
\draw[->,draw=green] (20) to node[auto,swap] {$\bar q \eta$} (11);
\draw[->,draw=green] (30) to node[auto,swap] {$\bar q \eta$} (21);
\draw[->,draw=green] (40) to node[auto,swap] {$\bar q \eta$} (31);
\draw[->,draw=green] (50) to node[auto,swap] {$\bar q \eta$} (41);
\end{tikzpicture}
\end{document}

Answer 1

Here's something, not in the most concise form, to get you started. In fact, I think almost all the commands you need for your diagram are here. Here's the code:

\documentclass{standalone}

\usepackage{tikz}
\usetikzlibrary{shapes,arrows.meta}

\tikzstyle{mynode}=[ellipse,draw,inner xsep=.3cm,inner ysep=.2cm]
\tikzstyle{toparrow}=[->,transform canvas={yshift=4pt}]
\tikzstyle{bottomarrow}=[->,transform canvas={yshift=-4pt}]

\begin{document}

\begin{tikzpicture}[line width=1pt,>={Straight Barb[length=5pt,width=5pt]},shorten >=3pt,shorten <=3pt]
\node[mynode] (00) at (0,0) {$0,\color{blue}{0}$};
\node[mynode] (10) at (3,0) {$1,\color{blue}{0}$};
\node[mynode] (11) at (3,2) {$1,\color{red}{2}$};
\draw[toparrow] (00) to node[above] {$\lambda$} (10);
\draw[bottomarrow] (10) to node[below] {$\eta$} (00);
\draw[->] (10) to node[right] {$\phi$} (11);
\draw[->,draw=green] (11) to node[auto,swap] {$\bar p \mu$} (00);
\end{tikzpicture}

\end{document}

And here's the output:

Now adjust the styles to fit your needs. Your colors may need adjusting, which you can do with the help of this question. Also, the three dots command is $\dots$ and the other Greek symbol is $\theta$.

The documentation for TikZ is indeed voluminous, but it is excellently organized and indexed, so I'm not convinced you went through all of it and didn't find what you need!

Answer 2

The tikz-cd package, which provides the cd TikZ library was made specifically for drawing commutative diagrams. With this package the code becomes much smaller and, in my opinion, better readable. The arrows can be placed next to the label from which they emanate.

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{cd,shapes,arrows.meta}
\begin{document}
\begin{tikzcd}[
  cells={nodes={draw,ellipse,inner sep=2pt,outer sep=2pt}},
  column sep=scriptsize,row sep=large,
  arrow style=tikz,
  diagrams={>={Straight Barb[length=4pt,width=4pt]}}
  ]
  % First line
  0,\color{green}1 \ar[r,"\lambda"] &
  1,\color{green}1 \ar[r,"\lambda"] \ar[d,"\theta"] &
  2,\color{green}1 \ar[r,"\lambda"] \ar[d,"\theta"] &
  |[draw=none]| \cdots \ar[r] &
  L_e(1),\color{green}1 \ar[r,"\lambda"] \ar[d,"\theta"] &
  L_e(1)+1,\color{green}1 \ar[d,"\theta"] \\
  % Second line
  &
  1,\color{red}2 \ar[r,"\lambda",shift left] \ar[lu,"p\mu",green] \ar[ld,"\bar{p}\mu",green] &
  2,\color{red}2 \ar[r,"\lambda",shift left] \ar[l,"\mu",shift left] &
  |[draw=none]| \cdots \ar[r,shift left] \ar[l,"\mu",shift left] &
  L_e(2),\color{red}2 \ar[r,"\lambda",shift left] \ar[l,shift left] &
  L_e(2)+1,\color{red}2 \ar[r,"\lambda",shift left] \ar[l,"\mu",shift left] &
  L_e(2)+2,\color{red}2 \ar[r,"\lambda",shift left] \ar[l,"\mu",shift left] &
  |[draw=none]| \cdots \ar[r,shift left] \ar[l,"\mu",shift left] &
  L_e(2),\color{red}2 \ar[r,"\lambda",shift left] \ar[l,shift left] &
  L_e(2)+1,\color{red}2 \ar[l,"\mu",shift left] \\
  % Third line
  0,\color{cyan}0 \ar[r,"\lambda",shift left] &
  1,\color{cyan}0 \ar[r,"\lambda",shift left] \ar[l,"\eta",shift left] \ar[u,"\phi"] &
  2,\color{cyan}0 \ar[r,"\lambda",shift left] \ar[l,"q\eta",shift left] \ar[u,"\phi"] \ar[lu,"\bar{q}\eta",green] &
  |[draw=none]| \cdots \ar[r,shift left] \ar[l,"q\eta",shift left] \ar[lu,"\bar{q}\eta",green] &
  L_e(1),\color{cyan}0 \ar[r,"\lambda",shift left] \ar[l,shift left] \ar[u,"\phi"] \ar[lu,"\bar{q}\eta",green] &
  L_e(1)+1,\color{cyan}0 \ar[l,"q\eta",shift left] \ar[u,"\phi"] \ar[lu,"\bar{q}\eta",green] \\
\end{tikzcd}
\end{document}

In my opinion, this image can be greatly improved by choosing slightly different options

\begin{tikzcd}[
  cells={nodes={draw=gray,thin,rectangle,rounded corners}},
  row sep=large
  ]