Octilinear graph drawing

Question

I am trying to draw a graph that can only use edges that are either vertical, horizontal, or diagonal at 45 degrees. I am trying to make a graph with 6 vertices and 8 edges. I so far have this:

\begin{tikzpicture}[->,>=stealth',auto,node distance=3cm,
thick,main node/.style={circle,fill=black!30,draw,minimum size=1cm,inner sep=0pt]}]

\node[main node] (v) []{$v$};

\node[main node] (w) [below left of =v] {$w$};

\node[main node] (1)  [left of =v] {$1$};

\node[main node] (2) [above of =w]  {$2$};

\node[main node] (3) [below of =v ]  {$3$};

\node[main node] (4) [right of = w] {$4$};
\path[-]


(v) 

edge node {} (1)
edge node {} (2) 
edge node {} (3) 
edge node {} (4)

(w)  
edge node {} (1)
edge node {} (2) 
edge node {} (3) 
edge node {} (4);

\end{tikzpicture}

But I want it to look like the picture attached, where the pink and blue lines are octilinear.

It currently looks like this:

Any tips?

Answer 1

I'd place the nodes with explicit coordinates, using variables to express the symmetries. Note that you can scale the picture without recalculating the coordinates (see the option scale=2 of the tikzpicture environment).

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}
  [->, >=stealth', auto, thick,
   main node/.style=
     {circle, fill=black!30, draw, minimum size=1cm, inner sep=0pt]},
   scale=2
  ]
\newcommand\vx{0.5}
\newcommand\vy{1}
\newcommand\fx{2} % 4.x
\node[main node] (2) at (-\vx,  0 ) {$2$};
\node[main node] (3) at ( \vx,  0 ) {$3$};
\node[main node] (v) at ( \vx, \vy) {$v$};
\node[main node] (w) at (-\vx,-\vy) {$w$};
\node[main node] (1) at (-\fx, \vy) {$1$};
\node[main node] (4) at ( \fx,-\vy) {$4$};
\path[-]
  (v) edge node {} (1)
      edge node {} (2) 
      edge node {} (3) 
      edge node {} (4)
  (w) edge node {} (1)
      edge node {} (2) 
      edge node {} (3) 
      edge node {} (4);
\end{tikzpicture}
\end{document}

Answer 2

Well you could try reorganising which nodes you position relative to which

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows}

\begin{document}
\begin{tikzpicture}[->,>=stealth',auto,node distance=3cm,
thick,main node/.style={circle,fill=black!30,draw,minimum size=1cm,inner sep=0pt]}]

\node[main node] (v) []{$v$};
\node[main node] (2) [below left of =v]  {$2$};
\node[main node] (w) [below of =2] {$w$};
\node[main node] (1)  [above left of =2] {$1$};
\node[main node] (3) [below of =v]  {$3$};
\node[main node] (4) [below right of = 3] {$4$};
\path[-]

(v) 
edge node {} (1)
edge node {} (2) 
edge node {} (3) 
edge node {} (4)

(w)  
edge node {} (1)
edge node {} (2) 
edge node {} (3) 
edge node {} (4);

\end{tikzpicture}
\end{document}

Alternatively, while the relative positioning of TikZ can be quite helpful, if you have a specific position in mind you may like to position nodes explicitly, or use a matrix to place them on a grid a bit more naturally as in the example below.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{matrix}

\begin{document}
\begin{tikzpicture}[->,>=stealth',auto,node distance=3cm,
thick,main node/.style={circle,fill=black!30,draw,minimum size=1cm,inner sep=0pt]}]

\matrix (octilinear) [matrix of nodes,nodes={main node},column sep = 2cm,row sep = 2cm]
{
    1 & & & V & & \\
    & & 2 & 3 & & \\
    & & W & & & 4 \\
};

\draw[-] (octilinear-1-1) -- (octilinear-1-4);
\draw[-] (octilinear-1-4) -- (octilinear-2-4);
\draw[-] (octilinear-2-3) -- (octilinear-1-4);
\draw[-] (octilinear-2-3) -- (octilinear-3-3);
\draw[-] (octilinear-3-3) -- (octilinear-3-6);
\draw[-] (octilinear-2-4) -- (octilinear-3-3);
\draw[-] (octilinear-1-1) -- (octilinear-3-3);
\draw[-] (octilinear-1-4) -- (octilinear-3-6);

\end{tikzpicture}
\end{document}