Topological analysis of large scale protein-protein interaction networks (PINs) is important for understanding the organizational and functional principles of individual proteins. The number of interactions that a protein has in a PIN has been observed to be correlated with its indispensability. Essential proteins generally have more interactions than the nonessential ones. We show here that the lethality associated with removal of a protein from the yeast proteome correlates with different centrality measures of the nodes in the PIN, such as the closeness of a protein to many other proteins, or the number of pairs of proteins which need a specific protein as an intermediary in their communications, or the participation of a protein in different protein clusters in the PIN. These measures are significantly better than random selection in identifying essential proteins in a PIN. Centrality measures based on graph spectral properties of the network, in particular the subgraph centrality, show the best performance in identifying essential proteins in the yeast PIN. Subgraph centrality gives important structural information about the role of individual proteins, and permits the selection of possible targets for rational drug discovery through the identification of essential proteins in the PIN.