Phase retrieval generally refers to the nonlinear inverse problem of recovering a signal from phaseless linear measurements. We discuss a specific problem of this type, namely the question of recovering a function from its Gabor spectrogram (= modulus of its short-time Fourier transform with Gaussian window). As it is well-known this essentially amounts to asking 'can an entire function be determined from its modulus only?'. The focus of this talk lies on discussing stability properties of this problem, that is a quantitative notions of uniqueness. We will present results which characterize the stability of signals in terms of the connectivity of their spectrograms as measured by the Cheeger constant, a concept which plays an important role in Graph clustering.