Clustering coefficients of protein-protein interaction networks.

The properties of certain networks are determined by hidden variables that are not explicitly measured. The conditional probability (propagator) that a vertex with a given value of the hidden variable is connected to k other vertices determines all measurable properties. We study hidden variable models and find an averaging approximation that enables us to obtain a general analytical result for the propagator. Analytic results showing the validity of the approximation are obtained. We apply hidden variable models to protein-protein interaction networks (PINs) in which the hidden variable is the association free energy, determined by distributions that depend on biochemistry and evolution. We compute degree distributions as well as clustering coefficients of several PINs of different species; good agreement with measured data is obtained. For the human interactome two different parameter sets give the same degree distributions, but the computed clustering coefficients differ by a factor of about 2. This shows that degree distributions are not sufficient to determine the properties of PINs.