We employ the random graph theory approach to analyze the protein?protein interaction database DIP. Several global topological parameters are used to characterize the protein?protein interaction networks (PINs) for seven organisms. We find that the seven PINs are well approximated by the scale-free networks, that is, the node degree cumulative distribution Pcum(k) scales with the node degree k (Pcum(k) ~ k-?). We also find that the logarithm of the average clustering coefficient Cave(k) scales with k (Cave(k) ~ k-?), for E. coli and S. cerevisiae. In particular, we determine that the E. coli and the S. cerevisiae PINs are better represented by the stochastic and deterministic hierarchical network models, respectively. The current fruit fly protein?protein interaction dataset does not have convincing evidence in favor of the hierarchical network model. These findings lead us to conclude that, in contrast to scale-free structure, hierarchical structure model applies for certain species' PINs only.We also demonstrate that PINs are robust when subject to random perturbation where up to 50% of the nodes are rewired. Average node degree correlation study supports the fact that nodes of low connectivity are correlated, whereas nodes of high connectivity are not directly linked.
