I just discovered the feynMF package, a really neat tool for drawing Feynman diagrams.
I went ahead and drew a few diagrams which I'll include here just to set the right spirit for this question. I produced this

with this
\documentclass{article}
\usepackage{feynmf}
\begin{document}
$\begin{fmffile}{Diagram}
\begin{fmffile}{Diagram}
\begin{fmfgraph*}(40,15)
\fmfpen{thin}
\fmfleft{i}
\fmfright{o}
\fmf{plain}{i,o}
\fmfdot{i,o}
\fmfv{l.a=-90,l=$x$}{i}
\fmfv{l.a=-90,l=$y$}{o}
\end{fmfgraph*}
\quad + \quad
\begin{fmfgraph*}(40,15)
\fmfpen{thin}
\fmfleft{i}
\fmfright{o}
\fmf{plain}{i,v,v,o}
\fmfdot{i,o,v}
\fmfv{l.a=-90,l=$x$}{i}
\fmfv{l.a=-90,l=$y$}{o}
\fmfv{l.a=-90,l=$z$}{v}
\end{fmfgraph*}
\quad + \quad
\begin{fmfgraph*}(40,15)
\fmfpen{thin}
\fmfleft{i}
\fmfright{o}
\fmf{plain}{i,v1,v2,o}
\fmf{plain,left,tension=0.05}{v1,v2,v1}
\fmfdot{i,o,v1,v2}
\fmfv{l.a=-90,l=$x$}{i}
\fmfv{l.a=-90,l=$y$}{o}
\fmfv{l.a=-90}{v1,v2}
\fmflabel{$z_{1}$}{v1}
\fmflabel{$z_{2}$}{v2}
\end{fmfgraph*}
\quad + \enskip \dots
\end{fmffile}
\end{fmffile}$
\end{document}
Then I wanted to draw a few disconnected diagrams. This is where I got stuck. I'm trying to get this

Not very pretty I admit, but you get the idea, I hope. However, everything I tried so far did not compile. Is anybody sufficiently familiar with feynMF that could help me out here?

feynmp-auto? It issues the metapost run automatically so you do not have to do it yourself. No intermediate runs of metafont oder metapost anymore. – MaxNoe Dec 01 '14 at 22:23feynmp-auto. – Steven B. Segletes Dec 02 '14 at 00:28feynmp-autoyesterday. While writing this question Stackexchange suggested similar questions some of which I looked at. In this thread, egreg recommended the use offeynmp-autooverfeynmf. However, since I am using ShareLaTeX most of the time, this ordeal of compiling several times does not affect me. I'll still usefeynmp-autofrom now on since it's supposed to be easier. – Janosh Dec 02 '14 at 09:05