Elaborating the method proposed in my comment:
\documentclass[tikz]{standalone}
\usepackage{tikz}
\begin{document}
\foreach \n [remember=\n as \previous (initially 0)] in {1,...,7,0} {
\begin{tikzpicture}[main_node/.style={circle,fill=blue!20,draw,minimum size=2em,inner sep=3pt]}]
\node[main_node] (8) at (0:0.5) {b};
\node[main_node] (9) at (180:0.5) {t};
\foreach \x in {0,1,...,7}
\node[main_node] (\x) at (360/8*\x:2) {$a_{\x}$};
\path[draw,thick] (\n) edge (8);
\path[draw,thick] (\n) edge (9);
\path[draw,thick] (\previous) edge (8);
\path[draw,thick] (\previous) edge (9);
\path[draw,thick] (\n) edge (\previous);
\end{tikzpicture}
}
\end{document}
Result:

(Not sure if this is the intended result, but at least it can illustrate the proposed method)
Update: A little improvement to avoid overlapping edges (and to add the missing t--b edge):
\documentclass[tikz]{standalone}
\usepackage{tikz}
\begin{document}
\foreach \n [remember=\n as \previous (initially 0)] in {1,...,7,0} {
\begin{tikzpicture}[main_node/.style={circle,fill=blue!20,draw,minimum size=2em,inner sep=3pt]}]
\node[main_node] (8) at (0:0.5) {b};
\node[main_node] (9) at (180:0.5) {t};
\foreach \x in {0,1,...,7}
\node[main_node] (\x) at (360/8*\x:2) {$a_{\x}$};
\path[draw,thick] (\n) edge[bend left] (8);
\path[draw,thick] (\n) edge[bend right] (9);
\path[draw,thick] (8) edge (9);
\path[draw,thick] (\previous) edge[bend left] (8);
\path[draw,thick] (\previous) edge[bend right] (9);
\path[draw,thick] (\n) edge (\previous);
\end{tikzpicture}
}
\end{document}
Result:

Second update
Using a conditional expression, we can change the bending direction of the edges for the cases of the nodes a4..a7, which produces a nicer result.
\documentclass[tikz,border=2pt]{standalone}
\usepackage{tikz}
\begin{document}
\foreach \n [remember=\n as \previous (initially 7)] in {0,...,7} {
\begin{tikzpicture}[main_node/.style={circle,fill=blue!20,draw,minimum size=2em,inner sep=3pt]}]
\node[main_node] (8) at (0:0.5) {b};
\node[main_node] (9) at (180:0.5) {t};
\foreach \x in {0,1,...,7}
\node[main_node] (\x) at (360/8*\x:2) {$a_{\x}$};
% Here is the conditional which defines \up and \down
% appropiately, depending on the iteration of the loop
\pgfmathsetmacro{\up}{\previous < 4 ? "left" : "right"}
\pgfmathsetmacro{\down}{\previous < 4 ? "right" : "left"}
\path[draw,thick] (\n) edge[bend \up] (8);
\path[draw,thick] (\n) edge[bend \down] (9);
\path[draw,thick] (8) edge (9);
\path[draw,thick] (\previous) edge[bend \up] (8);
\path[draw,thick] (\previous) edge[bend \down] (9);
\path[draw,thick] (\n) edge (\previous);
\end{tikzpicture}
}
\end{document}
Result:

\begin{picture}/\end{picture}
is inside the loop, each iteration of it would produce a new figure. See my anser. – JLDiaz Feb 12 '17 at 17:49