Draw the following paths

Question

I want to draw the following paths. But I don't know how to start because I am new to this and I am learning. Can someone help me?

Answer 1

With use of the tikz package:

\documentclass[border=3.141592]{standalone}
\usepackage{tikz}
\usetikzlibrary{chains,
                positioning}
\begin{document}
    \begin{tikzpicture}[
node distance = 12mm,
  start chain = v going right,
     V/.style = {circle,draw, fill=blue, inner sep=1pt, 
            node contents={}, on chain},
every label/.append style = {font=\footnotesize\sffamily, text=blue}
                    ]
\foreach \x in {A, B, C, D}
    \node[V, label=\x];
%
\draw (v-1) to (v-2) 
      (v-1) to [bend left]  (v-2)
      (v-1) to [bend left=45]   (v-3)
      (v-1) to [bend right] (v-2)
      (v-1) to [bend right=45]  (v-2)
      (v-1) to [bend right=45]  (v-3)
      (v-2) to [bend left]  (v-3)
      (v-2) to [bend right] (v-3)
      (v-3) to [bend left]  (v-4)
      (v-3) to (v-4)
      (v-3) to [bend right] (v-4);
    \end{tikzpicture}
\end{document}

Answer 2

Here is a way to do it with pstricks:

\documentclass[border=6pt, svgnames]{standalone}
\usepackage{pst-eucl}
\begin{document}
\begin{pspicture}(-1,-1.5)(10,1.5)
\sffamily\color{Blue} \psset{PtNameMath=false}
\pstGeonodePosAngle={120,90,90,60}{A}(3,0){B}(6,0){C}(9,0){D}
\psline(A)(B) \psline(C)(D)
\pcarcarcangle=40(B)\pcarcarcangle=60(C)      \pcarcarcangle=40(D)
\pcarcarcangle=-30(B)\pcarcarcangle=-30(C)  \pcarcarcangle=-30(D)
\pcarcarcangle=60(C)\pcarcarcangle=-60(C)
\pcarcarcangle=-60(B)
\end{pspicture}
\end{document}