\documentclass[tikz,border=5pt]{standalone}
\usepackage{amsmath,amssymb,tikz,xcolor}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[thick,scale=1, every node/.style={transform shape}]
\tikzset{vertex/.style = {circle,fill=black,minimum size=5pt, inner sep=0pt}}
\tikzset{edge/.style = {->,> = latex'}}
\begin{scope}
\node[vertex, label=left:$v_{i+1}$] (vip1) at (0:0.45) {};
\node[vertex, label=left:$v_{i}$] (vi) at (120:1) {};
\node[vertex, label=left:$x_{i}$] (xi) at (-120:1) {};
\draw[edge] (xi) to (vi);
\draw[edge] (vi) to (vip1);
\draw[edge] (vip1) to (xi);
\begin{scope}[xshift=3cm]
\node[vertex, label=right:$v_{j+1}$] (vjp1) at (0:0.45) {};
\node[vertex, label=right:$v_{j}$] (vj) at (120:1) {};
\node[vertex, label=right:$x_{j}$] (xj) at (-120:1) {};
\draw[edge] (xj) to (vj);
\draw[edge] (vj) to (vjp1);
\draw[edge] (vjp1) to (xj);
\end{scope}
\draw[edge,dashed] (xi) to (xj);
\draw[edge,dashed] (vip1) to (vj);
\draw[edge,dashed] (vip1) to (vjp1);
\draw[edge,dashed] (vi) to (vj);
\draw[edge,dashed] (vi) to (vjp1);
\draw[edge] (vj) to (xi);
\draw[edge] (vjp1) to (xi);
\draw[edge] (xj) to (vi);
\draw[edge] (xj) to (vip1);
\node[] (a) at (1.3,-1.3) {$(a)$};
\end{scope}
\begin{scope}[xshift=7cm]
\node[vertex, label=left:$v_{i+1}$] (vip1) at (0:0.45) {};
\node[vertex, label=left:$v_{i}$] (vi) at (120:1) {};
\node[vertex, label=left:$x_{i}$] (xi) at (-120:1) {};
\draw[edge] (xi) to (vi);
\draw[edge] (vi) to (vip1);
\draw[edge] (vip1) to (xi);
\begin{scope}[xshift=3cm]
\node[vertex, label=right:$v_{j+1}$] (vjp1) at (0:0.45) {};
\node[vertex, label=right:$v_{j}$] (vj) at (120:1) {};
\node[vertex, label=right:$x_{j}$] (xj) at (-120:1) {};
\draw[edge] (xj) to (vj);
\draw[edge] (vj) to (vjp1);
\draw[edge] (vjp1) to (xj);
\end{scope}
\draw[edge,dashed] (vip1) to (vj);
\draw[edge,dashed] (vip1) to (vjp1);
\draw[edge,dashed] (vi) to (vj);
\draw[edge,dashed] (vi) to (vjp1);
\draw[edge] (xj) to (xi);
\draw[edge] (vj) to (xi);
\draw[edge] (vjp1) to (xi);
\draw[edge] (xj) to (vi);
\draw[edge] (xj) to (vip1);
\node[] (a) at (1.3,-1.3) {$(b)$};
\end{scope}
\begin{scope}[yshift=-3cm]
\node[vertex, label=left:$v_{i+1}$] (vip1) at (0:0.45) {};
\node[vertex, label=left:$v_{i}$] (vi) at (120:1) {};
\node[vertex, label=left:$x_{i}$] (xi) at (-120:1) {};
\draw[edge] (xi) to (vi);
\draw[edge] (vi) to (vip1);
\draw[edge] (vip1) to (xi);
\begin{scope}[xshift=3cm]
\node[vertex, label=right:$v_{j+1}$] (vjp1) at (0:0.45) {};
\node[vertex, label=right:$v_{j}$] (vj) at (120:1) {};
\node[vertex, label=right:$x_{j}$] (xj) at (-120:1) {};
\draw[edge] (xj) to (vj);
\draw[edge] (vj) to (vjp1);
\draw[edge] (vjp1) to (xj);
\end{scope}
\draw[edge,dashed] (vip1) to (vj);
\draw[edge,dashed] (vip1) to (vjp1);
\draw[edge,dashed] (vi) to (vj);
\draw[edge,dashed] (vi) to (vjp1);
\draw[edge,dashed] (xi) to (vj);
\draw[edge,dashed] (xi) to (xj);
\draw[edge,dashed] (xi) to (vjp1);
\draw[edge] (xj) to (vi);
\draw[edge] (xj) to (vip1);
\node[] (a) at (1.3,-1.3) {$(c)$};
\end{scope}
\begin{scope}[yshift=-3cm, xshift=7cm]
\node[vertex, label=left:$v_{i+1}$] (vip1) at (0:0.45) {};
\node[vertex, label=left:$v_{i}$] (vi) at (120:1) {};
\node[vertex, label=left:$x_{i}$] (xi) at (-120:1) {};
\draw[edge] (xi) to (vi);
\draw[edge] (vi) to (vip1);
\draw[edge] (vip1) to (xi);
\begin{scope}[xshift=3cm]
\node[vertex, label=right:$v_{j+1}$] (vjp1) at (0:0.45) {};
\node[vertex, label=right:$v_{j}$] (vj) at (120:1) {};
\node[vertex, label=right:$x_{j}$] (xj) at (-120:1) {};
\draw[edge] (xj) to (vj);
\draw[edge] (vj) to (vjp1);
\draw[edge] (vjp1) to (xj);
\end{scope}
\draw[edge,dashed] (xi) to (xj);
\draw[edge,dashed] (vip1) to (vj);
\draw[edge,dashed] (vip1) to (vjp1);
\draw[edge,dashed] (vi) to (vj);
\draw[edge,dashed] (vi) to (vjp1);
\draw[edge,dashed] (vi) to (xj);
\draw[edge,dashed] (vip1) to (xj);
\draw[edge] (vj) to (xi);
\draw[edge] (vjp1) to (xi);
\node[] (a) at (1.3,-1.3) {$(d)$};
\end{scope}
\begin{scope}[yshift=-6cm]
\node[vertex, label=left:$v_{i+1}$] (vip1) at (0:0.45) {};
\node[vertex, label=left:$v_{i}$] (vi) at (120:1) {};
\node[vertex, label=left:$x_{i}$] (xi) at (-120:1) {};
\draw[edge] (xi) to (vi);
\draw[edge] (vi) to (vip1);
\draw[edge] (vip1) to (xi);
\begin{scope}[xshift=3cm]
\node[vertex, label=right:$v_{j+1}$] (vjp1) at (0:0.45) {};
\node[vertex, label=right:$v_{j}$] (vj) at (120:1) {};
\node[vertex, label=right:$x_{j}$] (xj) at (-120:1) {};
\draw[edge] (xj) to (vj);
\draw[edge] (vj) to (vjp1);
\draw[edge] (vjp1) to (xj);
\end{scope}
\draw[edge,dashed] (vip1) to (vj);
\draw[edge,dashed] (vip1) to (vjp1);
\draw[edge,dashed] (vi) to (vj);
\draw[edge,dashed] (vi) to (vjp1);
\draw[edge,dashed] (vi) to (xj);
\draw[edge,dashed] (vip1) to (xj);
\draw[edge,dashed] (xi) to (vj);
\draw[edge,dashed] (xi) to (vjp1);
\draw[edge] (xj) to (xi);
\node[] (a) at (1.3,-1.3) {$(e)$};
\end{scope}
\begin{scope}[xshift=7cm,yshift=-6cm]
\node[vertex, label=left:$v_{i+1}$] (vip1) at (0:0.45) {};
\node[vertex, label=left:$v_{i}$] (vi) at (120:1) {};
\node[vertex, label=left:$x_{i}$] (xi) at (-120:1) {};
\draw[edge] (xi) to (vi);
\draw[edge] (vi) to (vip1);
\draw[edge] (vip1) to (xi);
\begin{scope}[xshift=3cm]
\node[vertex, label=right:$v_{j+1}$] (vjp1) at (0:0.45) {};
\node[vertex, label=right:$v_{j}$] (vj) at (120:1) {};
\node[vertex, label=right:$x_{j}$] (xj) at (-120:1) {};
\draw[edge] (xj) to (vj);
\draw[edge] (vj) to (vjp1);
\draw[edge] (vjp1) to (xj);
\end{scope}
\draw[edge,dashed] (vip1) to (vj);
\draw[edge,dashed] (vip1) to (vjp1);
\draw[edge,dashed] (vi) to (vj);
\draw[edge,dashed] (vi) to (vjp1);
\draw[edge,dashed] (vi) to (xj);
\draw[edge,dashed] (vip1) to (xj);
\draw[edge,dashed] (xi) to (vj);
\draw[edge,dashed] (xi) to (vjp1);
\draw[edge,dashed] (xi) to (xj);
\node[] (a) at (1.3,-1.3) {$(f)$};
\end{scope}
\begin{scope}[yshift=-9cm]
\node[vertex, label=left:$v_{i+1}$] (vip1) at (0:0.45) {};
\node[vertex, label=left:$v_{i}$] (vi) at (120:1) {};
\node[vertex, label=left:$x_{i}$] (xi) at (-120:1) {};
\draw[edge] (xi) to (vi);
\draw[edge] (vi) to (vip1);
\draw[edge] (vip1) to (xi);
\begin{scope}[xshift=3cm]
\node[vertex, label=right:$v_{j+1}$] (vjp1) at (0:0.45) {};
\node[vertex, label=right:$v_{j}$] (vj) at (120:1) {};
\node[vertex, label=right:$x_{j}$] (xj) at (-120:1) {};
\draw[edge] (xj) to (vj);
\draw[edge] (vj) to (vjp1);
\draw[edge] (vjp1) to (xj);
\end{scope}
\draw[edge,dashed] (vip1) to (vj);
\draw[edge,dashed] (vip1) to (vjp1);
\draw[edge,dashed] (vi) to (vj);
\draw[edge,dashed] (vi) to (vjp1);
\draw[edge,dashed] (vi) to (xj);
\draw[edge,dashed] (vip1) to (xj);
\draw[edge] (xj) to (xi);
\draw[edge] (vj) to (xi);
\draw[edge] (vjp1) to (xi);
\node[] (a) at (1.3,-1.3) {$(g)$};
\end{scope}
\begin{scope}[xshift=7cm,yshift=-9cm]
\node[vertex, label=left:$v_{i+1}$] (vip1) at (0:0.45) {};
\node[vertex, label=left:$v_{i}$] (vi) at (120:1) {};
\node[vertex, label=left:$x_{i}$] (xi) at (-120:1) {};
\draw[edge] (xi) to (vi);
\draw[edge] (vi) to (vip1);
\draw[edge] (vip1) to (xi);
\begin{scope}[xshift=3cm]
\node[vertex, label=right:$v_{j+1}$] (vjp1) at (0:0.45) {};
\node[vertex, label=right:$v_{j}$] (vj) at (120:1) {};
\node[vertex, label=right:$x_{j}$] (xj) at (-120:1) {};
\draw[edge] (xj) to (vj);
\draw[edge] (vj) to (vjp1);
\draw[edge] (vjp1) to (xj);
\end{scope}
\draw[edge,dashed] (vip1) to (vj);
\draw[edge,dashed] (vip1) to (vjp1);
\draw[edge,dashed] (vi) to (vj);
\draw[edge,dashed] (vi) to (vjp1);
\draw[edge,dashed] (xi) to (vj);
\draw[edge,dashed] (xi) to (vjp1);
\draw[edge] (xj) to (vi);
\draw[edge] (xj) to (vip1);
\draw[edge] (xj) to (xi);
\node[] (a) at (1.3,-1.3) {$(h)$};
\end{scope}
\end{tikzpicture}
\end{document}