Drawing a circular graph using xypic

Question

How can I draw a circular graph, as in the picture below, using xypic?

Answer 1

My it is only a comment instead of a true answer, because I think that with \xymatrix the way is very very long and with lot of difficulties.

\documentclass[a4paper,12pt]{article}
\usepackage[all]{xy}
\usepackage{newtxtext,newtxmath}

\begin{document}
\xymatrix{
G& {\overset{\displaystyle 1}{\bullet}}\ar@/^1pc/[dr]^{\alpha_1} &  \\
A& B& {\bullet}\ar@/^1pc/[dl]\\
D& E& F}
\end{document}

My problems are:

1. @{.} give me only dotted straight line and not curved arrows withouts tips. In addendum in the picture there are only 3 dots.
2. To put the rotated circle labels. For 1 it is very simple but for the others (????).
3. Create a fast circle loop (see the § 8.2 Circles and Ellipses of the complete/old documentation http://texdoc.net/texmf-dist/doc/generic/xypic/xyrefer.pdf).

I should read and to understood the manual and the commands that they are differents from the canonical but not very simple use of the arrows.