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Protein-interaction network (PIN) analysis provides valuable insight into an organism's functional organization and evolutionary behavior. In this paper, we study a PIN formed by high-confidence human protein interactions obtained from various public interaction databases. This is the largest human PIN studied to date, comprising nearly 18,000 proteins and 44,000 interactions. A novel contribution of this paper is the computation of betweenness centrality, a graph-theoretic metric that is found to be positively correlated with the essentiality and evolutionary age of a protein. We observe that proteins with high betweenness centrality, but low connectivity are abundant in the human PIN. We have designed an efficient and portable parallel implementation for the calculation of this compute-intensive centrality metric. On the Sun Fire T2000 server with the UltraSparc T1 (Niagara) processor, we achieve a relative speedup of about 16 using 32 threads for a typical instance of betweenness centrality, reducing the running time from several minutes to 13 seconds.