Biologically significant information can be revealed by modeling large-scale protein interaction data using graph theory based network analysis techniques. However, the methods that are currently being used draw conclusions about the global features of the network from local connectivity data. A more systematic approach would be to define global quantities that measure (1) how strongly a protein ties with the other parts of the network and (2) how significantly an interaction contributes to the integrity of the network, and connect them with phenotype data from other sources. In this paper, we introduce such global connectivity measures and develop a stochastic algorithm based upon percolation in random graphs to compute them.