How to draw a diagram with arrows?

Question

I want to draw the following diagram in LaTeX:

Answer 1

For the sake of completeness, here it is a plain TikZ approach

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{positioning}
\begin{document}
    \begin{tikzpicture}[node distance = 2cm, thick]% 
        \node (1) {1};
        \node (2) [right=of 1] {2};
        \node (3) [right=of 2] {3};
        \draw[->] (1) -- node [midway,above] {a} (2);
        \draw[->] (1) to [bend right] node [midway,below]{c} (3);
        \draw[->] (2) -- node [midway,above] {b} (3);
    \end{tikzpicture}%
\end{document}

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{positioning}
\begin{document}
    \begin{tikzpicture}[node distance = 2cm, thick]% 
        \node (1) {1};
        \node (2) [right=of 1] {2};
        \node (3) [right=of 2] {3};
        \node (dots) [right=of 3] {$\cdots$};
        \node (n1) [right=of dots] {$n-1$};
        \node (n) [right=of n1] {$n$};
        %
        \draw[->] (1) -- node [midway,above] {$a_1$} (2);
        \draw[->] (1) to [bend right=15cm] node [midway,below]{b} (n);
        \draw[->] (2) -- node [midway,above] {$a_2$} (3);
        \draw[->] (3) -- node [midway,above] {$a_3$} (dots);
        \draw[->] (dots) -- node [midway,above] {$a_{n-2}$} (n1);
        \draw[->] (n1) -- node [midway,above] {$a_{n-1}$} (n);
    \end{tikzpicture}%
\end{document}

Answer 2

It's quite easy with tikz-cd:

\documentclass{article}
\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}
1 \ar[r,"a"] \ar[rr,bend right,"c"'] & 2 \ar[r,"b"] & 3
\end{tikzcd}
\end{document}

But, in my humble opinion, I'd vote for picture-mode, for its far more user-friendly syntax:

\documentclass{article}
\usepackage{pict2e}
\begin{document}
\setlength{\unitlength}{1cm}
\begin{picture}(2.1,0.75)(0,-0.45)
\put(0,0){1}
  \put(0.2,0.1){\vector(1,0){0.75}}
  \put(0.5,0.15){\footnotesize$a$}
\put(1,0){2}
  \put(1.2,0.1){\vector(1,0){0.75}}
  \put(1.5,0.15){\footnotesize$b$}
\put(2,0){3}
  \qbezier(0.2,-0.05)(1.05,-0.7)(1.9,-0.05)
  \put(1.9,-0.05){\vector(4,3){0.0001}}
  \put(1.0,-0.55){\footnotesize$c$}
\end{picture}
\end{document}

---

Update: tikz-cd solution for the second diagram:

\documentclass{article}
\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}
  1 \ar[r,"a_1"]
    \ar[rrrrr,bend right=50,looseness=0.3,"b"']
& 2 \ar[r,"a_2"]
& 3 \ar[r,"a_3"]
& \cdots
  \ar[r,"a_{n-2}"] % This arrow isn't in the picture, but I chose to add it. Feel free to remove.
& n-1 \ar[r,"a_{n-1}"]
& n
\end{tikzcd}
\end{document}

Answer 3

A pstrickssolution: the three numbers are defined as nodes, and we link them by node connections.

\documentclass[12pt]{article}
\usepackage{pst-node, auto-pst-pdf}

\begin{document}

\[
  \Rnode{1}{1} \hspace{3em} \Rnode{2}{2} \hspace{3em} \Rnode{3}{3}
\psset{linewidth=0.6pt, arrows=->, arrowinset=0.12, nodesep=0.6ex, labelsep=2pt, shortput=nab}
\everypsbox{\scriptstyle}
\ncline{1}{2}^{a}\ncline{2}{3}^{b}
\ncarc[arcangle=-30]{1}{3}_{c}
\]

\end{document} 

Answer 4

With TikZ, it is possible to use the chain concept of the graphs library.

chains are a series of nodes whose syntax is abbreviated compared to their normal syntax. A chain ends with a semicolon. The nodes and their text are identical by default as in the first figure. Nodes and text are the number 1, 2 and 3.

This first figure is composed of 2 chains: the first 1->2->3 and the second which goes directly from 1 to 3.

To add text to the arrow (that is called edge by tikz), simply place the option edge label or edge label' depending on whether the text is above or below the arrow. In reality, this places the text to the left or right when walking in the direction of the chain.

In the second example, to avoid having to draw an arrow, we write -!- instead of -> (see section 19.3.3 Syntax of Chain Specifications page 272 of 3.1.1 TikZ manual). To make the node text different from its name, simply separate the name from the text with a slash. For example : 5/{$n-1$} means that node 5 displays the n-1 text.

With the quotes library:

Using the quotes library, the syntax for writing labels is even shorter: "a" instead of edge label={a} "c"' instead of edge label' ={c} You can customize the colors as below:

\documentclass[a4paper,12pt]{article}
\usepackage{tikz}
\usetikzlibrary{graphs,quotes}
\begin{document}

\tikz[thick,gray] \graph[grow right=30mm] {
1 ->["a"] 2   ->["b"] 3;
1 -> [bend right,"c"'] 3;
};

General case:
\smallskip

\tikz[thick,every edge/.style={red,draw},every node/.style={blue}] \graph[grow right=20mm,edge quotes={black,auto}] {
1 ->["$a_1$"] 2   ->["$a_2$"] 3->["$a_3$"] 4/$\cdots$   -!- 5/{$n-1$}->["$a_{n-1}$"] n  ;
1 -> [bend right,"b"'] n;
};

\end{document}

Without the quotes library

\documentclass[a4paper,12pt]{article}
\usepackage{tikz}
\usetikzlibrary{graphs}
\begin{document}

\tikz \graph[grow right=30mm] {
1 ->[edge label={a}] 2   ->[edge label={b}] 3;
1 -> [bend right,edge label'={c}] 3;
};


\tikz \graph[grow right=20mm] {
1 ->[edge label={$a_1$}] 2   ->[edge label={$a_2$}] 3->[edge label={$a_3$}] 4/$\cdots$   -!- 5/{$n-1$}->[edge label={$a_{n-1}$}] n  ;
1 -> [bend right,edge label'={b}] n;
};

\end{document}

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