How to make the edge not intercept a vertex

Question

I have a question about how to make an edge not necessarily, that is, there is a white "margin" between the vertex and the intersecting edge.

Note that in this image there is a space around the vertex

Answer 1

You only need to set some outer sep.

\documentclass[tikz,border=3mm]{standalone}
\begin{document}
\begin{tikzpicture}[Dot/.style={circle,fill,inner sep=1.5pt,outer sep=0.5pt}]
\path[rotate=20,nodes={Dot},thick] foreach \X in {1,2,3} {(\X*90-90:0.5) node (\X){}}
(270:1.5) node(4){} (1) foreach \X in {2,3,4} {edge (\X)}
 (3) edge (2) edge (4) (2) edge (4);
\path[xshift=2cm,rotate=20,nodes={Dot,outer sep=1.5pt},thick] foreach \X in {1,2,3} {(\X*90-90:0.5) node (\X){}}
(270:1.5) node(4){} (1) foreach \X in {2,3,4} {edge (\X)}
 (3) edge (2) edge (4) (2) edge (4);
\end{tikzpicture}
\end{document}