How can I move an edge connecting two nodes?

Question

I predefined the nodes and now the edges are connecting the nodes as follows:

\documentclass {scrartcl}
\usepackage{tikz}
\begin{document}
\begin{center}
\begin{tikzpicture}

    \tikzstyle{vertex} = [ color=black, text=black, fill=black!10]
    \tikzstyle{edge} = [thick]
% place nodes
\node[draw]  [vertex] at (0, 3)   (a) {Node 6};
\node[draw] [vertex] at (1, 4)   (b) {Node 12};
\node[draw] [vertex] at (2, 3)  (c)     {Node 19};
\node[draw] [vertex] at (3, 1)  (e)     {Node 20};
\node[draw] [vertex] at (4,3)  (d)     {Node 18};
\node[draw] [vertex] at (4,7)  (f)     {Node 10};
\node[draw] [vertex] at (6,1)  (g)     {Node 4};
\node[draw] [vertex] at (6,3)  (h)     {Node 2};
\node[draw] [vertex] at (6,6)  (i)     {Node 13};
\node[draw] [vertex] at (6,8)  (j)     {Node 14};
\node[draw] [vertex] at (7,3)  (k)     {Node 21};
\node[draw] [vertex] at (7,4)  (l)     {Node 1};
\node[draw] [vertex] at (7,7)  (m)     {Node 16};
\node[draw] [vertex] at (8,3)  (n)     {Node 3};
\node[draw] [vertex] at (8,9)  (o)     {Node 8};
\node[draw] [vertex] at (9,2)  (p)     {Node 5};
\node[draw] [vertex] at (9,5)  (q)     {Node 9};
\node[draw] [vertex] at (5,1)  (r)     {Node 11};
\node[draw] [vertex] at (7,-1)  (s)     {Node 7};
\node[draw] [vertex] at (8,-3)  (t)     {Node 17};
\node[draw] [vertex] at (9,-5)  (u)     {Node 22};
\node[draw] [vertex] at (5,-3)  (v)     {Node 15};



%Draw edges 
\draw[edge][color=red] (o)--(m)--(i)--(h)--(d)--(e)--(r)--(v);
\draw[edge][color=purple] (j)--(i)--(h)--(g)--(s)--(t)--(u);
\draw[edge][color=blue] (f)--(i)--(h)--(k)--(n)--(q);
\draw[edge][color=green] (l)--(h)--(d)--(b);
\draw[edge][color=yellow] (b)--(d)--(e)--(r)--(g)--(s)--(t)--(u);
\end{tikzpicture}
\end{center}

\end{document}
\end{document}

When two edges connect the same nodes, I would like to see both lines and not just one, so I want to shift one line for some mm. How can I achieve that?

Answer 1

[Expanded from my comment below, after some further testing :] It is possible to shift the starting and endpoints using xshift and yshift, but also the north/south/east/west (NSWE) anchors (you are "anchoring" these points to the NSEW sides of the vertices) :

\draw[edge, color=red] ([xshift=1pt]i.south)--([xshift=1pt]h.north);
\draw[edge, color=purple] (i)--(h);
\draw[edge, color=blue] ([xshift=-1pt]i.south)--([xshift=-1pt]h.north);

This above code will shift the red line 1pt to the right and the blue line 1pt to the left.

One downfall of this is that you must probably specify each shifted path separate of the general paths. In the example below, the shifted paths are drawn with a dashed pattern.

Then, I mentioned the positioning tikz library. You could avoid node overlaps with relative positioning; a quick example of the core of the figure :

    \node[vertex] (h) at (0,0) {Node 2h};
    \node[vertex] (i) [above= 3cm of h] {Node 13i};
    \node[vertex] (f) [above left= of i] {node 10f};
    \node[vertex] (j) [above= of i] {Node 14j};
    \node[vertex] (k) [right= of h] {Node 21k};
    \node[vertex] (l) [above right= of h] {Node 1l};
    \node[vertex] (m) [above right= of i] {Node 16m};
    \node[vertex] (n) [right= of k] {Node 3n};
    \node[vertex] (g) [below= of h] {Node 4g};
    \node[vertex] (d) [left=of h] {Node 18d};
%%%%%% Paths are grouped by color %%%%%%%
\draw[edge, color=red] (m) -- (i);
\draw[edge, color=red, dashed] ([xshift=1pt]i.south) -- ([xshift=1pt]h.north);
\draw[edge, color=red, dashed] ([yshift=1pt]h.west) -- ([yshift=1pt]d.east);

\draw[edge, color=purple] (j) -- (i) -- (h) -- (g);

\draw[edge, color=blue] (f) -- (i);
\draw[edge, color=blue, dashed] ([xshift=-1pt]i.south) -- ([xshift=-1pt]h.north);
\draw[edge, color=blue] (h) -- (k) -- (n);

\draw[edge, color=green] (l) -- (h) -- (d);

gives the following figure :

As one can see, the distance between nodes is pretty much always the same, except for node 13i where it is specified (any unit will do). One can also set this distance for the whole figure by appending [node distance = .5em, auto] after your \begin{tikzpicture}.

I hope this covers pretty much all !