Consider the 2 point function in $\phi^4$ theory which is given as something proportional to $$\int D(x-z) D(y-z) D(z-z) d^4 z,$$ where $D$ is the propagator. The corresponding Feynman diagram looks like this:
I understand where this comes from, but one thing I cannot figure out is why the vertex at $z$ is not connected to 4 propagators. Since the interaction term in the Lagrangian is $\phi^4$ shouldn't every vertex have 4 lines going into/out of it? Here there are only 3: $D(x-y)$, $D(z-y)$, and the loop $D(z-z)$. Are such loops counted twice? If so, why?