Can we define a multiedge command using tikz?

Question

I usually need to draw graphs with multiple edges. I would really appreciate if someone can tell me how to write a multiple edge command which will allow me to write one line instead of repeatedly many. Say the name of my edge command is \myedge[m] meaning that I will draw m edges between two nodes.

I want to use something like the following whenever I need to draw a multiple edge (multiplicity is 5 in the following)

\draw (a) \myedge[5] (b); 

Here is my actual code example... It is troublesome to keep using it in graphs where I have to keep drawing edges.

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{center}

\begin{tikzpicture}
\node[circle,fill=black,inner sep=1.5pt,draw] (a) at (180:1cm) {};
\node[circle,fill=black,inner sep=1.5pt,draw] (b) at (0:1cm) {};
\draw[thick] (a) -- (b);
\end{tikzpicture}

\begin{tikzpicture}
\node[circle,fill=black,inner sep=1.5pt,draw] (a) at (180:1cm) {};
\node[circle,fill=black,inner sep=1.5pt,draw] (b) at (0:1cm) {};
\draw[thick] (a) edge[bend left=5] (b);
\draw[thick] (a) edge[bend right=5] (b);
\end{tikzpicture}

\begin{tikzpicture}
\node[circle,fill=black,inner sep=1.5pt,draw] (a) at (180:1cm) {};
\node[circle,fill=black,inner sep=1.5pt,draw] (b) at (0:1cm) {};
\draw[thick] (a) edge[bend left] (b);
\draw[thick] (a) edge (b);
\draw[thick] (a) edge[bend right] (b);
\end{tikzpicture}

\begin{tikzpicture}
\node[circle,fill=black,inner sep=1.5pt,draw] (a) at (180:1cm) {};
\node[circle,fill=black,inner sep=1.5pt,draw] (b) at (0:1cm) {};
\draw[thick] (a) edge[bend left=15] (b);
\draw[thick] (a) edge[bend left=5] (b);
\draw[thick] (a) edge[bend right=5] (b);
\draw[thick] (a) edge[bend right=15] (b);
\end{tikzpicture}

\begin{tikzpicture}
\node[circle,fill=black,inner sep=1.5pt,draw] (a) at (180:1cm) {};
\node[circle,fill=black,inner sep=1.5pt,draw] (b) at (0:1cm) {};
\draw[thick] (a) edge[bend left=16] (b);
\draw[thick] (a) edge[bend left=8] (b);
\draw[thick] (a) edge[bend right=8] (b);
\draw[thick] (a) edge[bend right=16] (b);
\draw[thick] (a) -- (b);
\end{tikzpicture}
\end{center}
\end{document}

Output:

SITUATION: Here is what exactly I want to do in this new definition: Say, I would like to bend perpendicular to the line connecting two nodes (u) and (v) with coordinates (a,b) and (c,d). This gives me the chance to use ((c-a)*0.2*\i,(d-b)*0.2*\i) instead of $(0,0.2*\i)$ and it is most general. However, I can see that the bigger trouble here is that in defining edge[me=<number>] you actually do not account the ends of the edge. Can we do that?

This would certainly prevent the curly edges when edges are not on a horizontal line (it is worst when they are vertical actually). On the other hand, depending on how big is r=\sqrt{(c-a)^2+(d-b)^2} is, we might need to replace 0.2 with a much smaller/larger number. Maybe it is a good idea even to replace 0.2 with \frac{0.2}{r}.

Answer 1

Update

Now it's better. If A and B are the vertices and M the middle of AB, you need to determine two points P and Q such as PM orthogonal to AM and QM orthogonal to AM. Then you can draw the curve from A to B with a good control point.

If you want to draw multi edges between vertices at any position you need to use the curveto command like in the next code

\documentclass{article}
\usepackage{tikz} 
 \usetikzlibrary{calc} 
\begin{document}

\tikzset{me/.style={to path={
\pgfextra{% 
 \pgfmathsetmacro{\startf}{-(#1-1)/2}  
 \pgfmathsetmacro{\endf}{-\startf} 
 \pgfmathsetmacro{\stepf}{\startf+1}}
 \ifnum 1=#1 -- (\tikztotarget)  \else
     let \p{mid}=($(\tikztostart)!0.5!(\tikztotarget)$) 
         in
\foreach \i in {\startf,\stepf,...,\endf}
    {%
     (\tikztostart) .. controls ($ (\p{mid})!\i*6pt!90:(\tikztotarget) $) .. (\tikztotarget)
      }
      \fi   
     \tikztonodes
}}}   

\begin{tikzpicture}
\node[circle,fill=black,inner sep=1.5pt,draw] (a) at (1,1) {};
\node[circle,fill=black,inner sep=1.5pt,draw] (b) at (5,3) {};
\draw[thick] (a) edge[me=5] (b); 
\end{tikzpicture}      
\end{document} 

First answer

I define a new option mebut you can change the name. You need only to write [me=<number> ] It's possible to use an argument to modify 0.2 in 0.2*\i.

\documentclass{article}
\usepackage{tikz} 
 \usetikzlibrary{calc} 
\begin{document}

\tikzset{me/.style={to path={
\pgfextra{% 
 \pgfmathsetmacro{\startf}{-(#1-1)/2}  
 \pgfmathsetmacro{\endf}{-\startf} 
 \pgfmathsetmacro{\stepf}{\startf+1}}
 \ifnum 1=#1 -- (\tikztotarget)  \else
\foreach \i in {\startf,\stepf,...,\endf}
    {%
     (\tikztostart)        parabola[bend pos=0.5] bend +(0,0.2*\i)  (\tikztotarget)
      }
      \fi   
     \tikztonodes
      }}}   

 \begin{center}   
\begin{tikzpicture}
\node[circle,fill=black,inner sep=1.5pt,draw] (a) at (180:1cm) {};
\node[circle,fill=black,inner sep=1.5pt,draw] (b) at (0:1cm) {};
\draw[thick] (a) edge[me=1] (b); 
\end{tikzpicture}  

\begin{tikzpicture}
\node[circle,fill=black,inner sep=1.5pt,draw] (a) at (180:1cm) {};
\node[circle,fill=black,inner sep=1.5pt,draw] (b) at (0:1cm) {};
\draw[thick] (a) edge[me=2] (b); 
\end{tikzpicture} 

\begin{tikzpicture}
\node[circle,fill=black,inner sep=1.5pt,draw] (a) at (180:1cm) {};
\node[circle,fill=black,inner sep=1.5pt,draw] (b) at (0:1cm) {};
\draw[thick] (a) edge[me=3] (b); 
\end{tikzpicture}  
 
\begin{tikzpicture}
\node[circle,fill=black,inner sep=1.5pt,draw] (a) at (180:1cm) {};
\node[circle,fill=black,inner sep=1.5pt,draw] (b) at (0:1cm) {};
\draw[thick] (a) edge[me=5] (b); 
\end{tikzpicture}
\end{center}

\end{document}