Drawing arrows next to edges on graphs

Question

I need to draw several graphs (the graph theory kind) with arrows drawn next to the edges. Here is a rough sketch of the kind of thing I mean:

I'm aware of tkz-graph and would like to use it if possible - I have looked through its manual (I don't understand French but I can understand the code examples) but I don't see anything like this.

Alternatively I'm happy to use just plain tikz to do it, but I don't know how to draw things parallel to the edges in this way. (I want to do it automatically, not position the arrows by hand.)

Is there a straightforward way to do it, either in tkz-graph or just in tikz?

Answer 1

A pure TikZ solution with help of `mathtools˙package:

\documentclass[tikz,border=3mm]{standalone}
    \usetikzlibrary{chains,positioning}
    \usepackage{mathtools}

\begin{document}
\begin{tikzpicture}[
    start chain = A going right,
                    ]
    \begin{scope}[every node/.style={circle, draw, minimum size=1.5em, 
                                     inner sep=2pt, on chain}] 
\foreach \i in {1,...,5} \node {};
%
\node (B-1) [below=of A-2] {A};
\node (B-2) [below=of A-4] {B};
    \end{scope}
    \begin{scope}[every node/.style={above, sloped}]
\draw[densely dotted, thick] 
                (A-1) -- (A-2)
                (A-2) -- node {$\xleftarrow{1}$}  (A-3)
                (A-3) -- (A-4)
                (A-4) -- node {$\xleftarrow{1}$} (A-5);
\draw[thick]    (B-1) -- node {$\xleftarrow{1}$} (A-2)
                (B-1) -- node {$\xrightarrow{1}$}(A-3)
%
                (B-2) -- node[below] {$\xleftarrow[1]{}$} (A-3)
                (B-2) -- node {$\xleftarrow{1}$} (A-4)
                ;
%
\draw[double]   (A-1) --  (B-1)  
                (A-5) -- node[below] {$\xleftarrow[2]{}$} (B-2);
    \end{scope}
\end{tikzpicture}
\end{document}

Addendum: An alternative solution with help of pic:

\documentclass[tikz,border=3mm]{standalone}
    \usetikzlibrary{arrows.meta,chains,positioning}

\begin{document}
\begin{tikzpicture}[
    start chain = A going right,
pics/AB/.style args = {#1/#2/#3}{code={
    \draw[solid,-{Straight Barb[length=1mm]},very thick]
        (-3mm,#1 2mm) -- node [#2,font=\footnotesize,inner sep=2pt] {#3} ++ (6mm,0mm);}
                            },
pics/BA/.style args = {#1/#2/#3}{code={
    \draw[solid,{Straight Barb[length=1mm]}-,very thick]
        (-3mm,#1 2mm) -- node [#2,font=\footnotesize,inner sep=2pt] {#3} ++ (6mm,0mm);}
                            }
                    ]
    \begin{scope}[every node/.style={circle, draw, minimum size=1.5em, 
                                     inner sep=2pt, on chain}] 
\foreach \i in {1,...,5} \node {};
%
\node (B-1) [below=of A-2] {A};
\node (B-2) [below=of A-4] {B};
    \end{scope}
    \begin{scope}[sloped]
\draw[densely dotted, thick] 
                (A-1) -- (A-2)
                (A-2) -- pic {BA=/above/1} (A-3)%node {$\xleftarrow{1}$}  (A-3)
                (A-3) -- (A-4)
                (A-4) -- pic {AB=/above/1} (A-5);
\draw[thick]    (B-1) -- pic {AB=/left/1} (A-2)
                (B-1) -- pic {AB=-/above left/1} (A-3)
%
                (A-3) -- pic {BA=-/below left/1} (B-2)
                (B-2) -- pic {AB=/left/1} (A-4);
%
\draw[double]   (A-1) --  (B-1)  
                (A-5) -- pic {BA=-/below right/2} (B-2);
    \end{scope}
\end{tikzpicture}
\end{document}

Edit: in the first version of addendum I mess up the arrow directions. Now this is corrected.