  We present a simple model for the underlying structure of protein-protein
pairwise interaction graphs that is based on the way in which proteins attach
to each other in experiments such as yeast two-hybrid assays. We show that data
on the interactions of human proteins lend support to this model. The frequency
of the number of connections per protein under this model does not follow a
power law, in contrast to the reported behaviour of data from large scale yeast
two-hybrid screens of yeast protein-protein interactions. Sampling sub-graphs
from the underlying graphs generated with our model, in a way analogous to the
sampling performed in large scale yeast two-hybrid searches, gives degree
distributions that differ subtly from the power law and that fit the observed
data better than the power law itself. Our results show that the observation of
approximate power law behaviour in a sampled sub-graph does not imply that the
underlying graph follows a power law.
