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We employ the random graph theory approach to analyze the protein-protein interaction database DIP, for seven species. Several global topological parameters are used to characterize the protein-protein interaction networks (PINs) for each species. We find that the seven PINs are well approximated by the scale-free networks and the hierarchical models possibly except fruit fly. In particular, we determine that the E. coli and the yeast PINs are well represented by the stochastic and deterministic hierarchical network models respectively. These results suggesting that the hierarchical network model is a better description for certain species' PINs, and it may not be an universal feature across different species. Furthermore, we demonstrate that PINs are quite robust when subject to random perturbation where up to 50% of the nodes are rewired or removed or 50% of edges are removed. Average node degree correlation study supports the fact that nodes of low connectivity are correlated, whereas nodes of high connectivity are not directly linked.