This is a good start for arcs:
\documentclass[tikz,border=5mm]{standalone}
\begin{document}
\begin{tikzpicture}
\fill[black] (0,0) circle (1pt) (4,0) circle (1pt) (8,0) circle (1pt);
\draw (0,0)--(4,0) node[midway,above] {$e_0$};
\draw (4,0) to[out=90,in=90] node[midway,above] {$e_4$} (8,0);
\draw (4,0) to[out=30,in=150] node[midway,above] {$e_2$} (8,0);
\draw (4,0) -- node[midway,below] {$e_1$} (8,0);
\draw (4,0) to[out=-60,in=-120] node[midway,below] {$e_3$} (8,0);
\end{tikzpicture}
\end{document}

If you have defined the node formats before, you have to put the \draw
commands to a scope
, where you redefine the nodes:
\documentclass[tikz,border=5mm]{standalone}
\begin{document}
\begin{tikzpicture}
\fill[black] (0,0) circle (1pt) (4,0) circle (1pt) (8,0) circle (1pt);
\begin{scope}[every node/.style={fill=none,draw=none}]
\draw (0,0)--(4,0) node[midway,above] {$e_0$};
\draw (4,0) to[out=90,in=90] node[midway,above] {$e_4$} (8,0);
\draw (4,0) to[out=30,in=150] node[midway,above] {$e_2$} (8,0);
\draw (4,0) -- node[midway,below] {$e_1$} (8,0);
\draw (4,0) to[out=-60,in=-120] node[midway,below] {$e_3$} (8,0);
\end{scope}
\end{tikzpicture}
\end{document}
Bonus | The second figure:
\documentclass[tikz,border=5mm]{standalone}
\usetikzlibrary{angles,quotes}
\begin{document}
\begin{tikzpicture}
\draw[->] (-1,0)--(5.5,0);
\draw (0,-.5)--(0,4);
\coordinate (o) at (0,0);
\coordinate (a) at (3,0);
\coordinate (c) at (1,3);
\coordinate (b) at (4,2);
\coordinate (bx) at (5,2);
\coordinate (cx) at (2,3);
\coordinate (ax) at (5,0);
\draw[very thick] (o)--(a);
\draw[very thick] (a)--(b) node[midway,above left] {$\varphi'_B$};
\draw[very thick] (b)--(c) node[midway,below] {$\varphi'_A$};
\draw[very thick] (c)--(o) node[midway,right] {$\varphi'_I$};
\draw[dashed] (b)--(bx) (c)--(cx);
\pic[draw,"$\alpha_3$",angle radius=0.3cm,angle eccentricity=2] {angle=ax--a--b};
\pic[draw,"$\alpha_1$",angle radius=0.2cm,angle eccentricity=2] {angle=cx--c--o};
\pic[draw,"$\alpha_2$",angle radius=0.2cm,angle eccentricity=2] {angle=bx--b--c};
\end{tikzpicture}
\end{document}

You need the angles
library for angle notations and quotes
library to insert the angle names.