We develop a stochastic model for quantifying the binary measurements of protein-protein interactions. A key concept in the model is the binary response function (BRF) which represents the conditional probability of successfully detecting a protein-protein interaction with a given number of the protein complexes. A popular form of the BRF is introduced and the effect of the sharpness (Hill's coefficient) of this function is studied. Our model is motivated by the recently developed yeast two-hybrid method for measuring protein-protein interaction networks. We suggest that the same phenomenological BRF can also be applied to the mass spectroscopic measurement of protein-protein interactions. Based on the model, we investigate the contributions to the network topology of protein-protein interactions from (i) the distribution of protein binary association free energy, and from (ii) the cellular protein abundance. It is concluded that the association constants among different protein pairs cannot be totally independent. It is also shown that not only the association constants but also the protein abundance could be a factor in producing the power-law degree distribution of protein-protein interaction networks.