# In Srednicki's book, when calculating loop corrections to the propagator, why doesn't he include both diagram topologies at second order?

This might be a somewhat basic question, so apologies in advance for that. I've only recently started learning QFT, and so I'd really like to make sure I understand this. In Srednicki's textbook, in chapter 14 Loop Corrections to the Propagator, he discusses the corrections to the full propagator in $$\phi^{3}$$-theory. This is how he begins:

The issue I'm having is understanding why equation $$(14.2)$$ takes that form. I agree with the $$\mathcal{O}(g^{0})$$ term, but for the $$\mathcal{O}(g^{2})$$ term given by $$\frac{1}{i}\tilde{\Delta}(k^{2})\left[i\Pi(k^{2})\right]\frac{1}{i}\tilde{\Delta}(k^{2}).$$ I'm a little unconvinced. For the exact 2-point propagator in $$\phi^{3}$$-theory, at this order, we have two distinct connected diagram topologies, given in chapter 9:

Unless I'm misunderstanding/miscalculating, the aforementioned term only takes into account the first of these diagrams, and not the second. The value of this diagram is explicitly $$\frac{1}{2}(ig)^{2}\left(\frac{1}{i}\right)^{2}\left(\frac{1}{i}\tilde{\Delta}(k^{2})\right)\left[\int\frac{d^{d}l}{(2\pi)^{d}}\,\tilde{\Delta}((l+k)^{2})\tilde{\Delta}(l^{2})\right]\left(\frac{1}{i}\tilde{\Delta}(k^{2})\right),$$ which is indeed the expression in $$(14.2),$$ but why do we not get a contribution from other diagram here as well? Shouldn't the propagator take into account all the possible diagram topologies?

Any help clarifying this would be much appreciated!

The second diagram in Fig. 9.6 is a tadpole diagram, which is zero due to the renormalization condition $$\langle \phi(x)\rangle_{J=0}~=~0 \tag{9.2},$$ cf. e.g. my Phys.SE answer here or the last paragraph on p. 67 in Srednicki.