The world of Big Data is changing dramatically right before our eyes-from the amount of data being produced to the way in which it is structured and used. The trend of 'big data growth' presents enormous challenges, but it also presents incredible scientific and business opportunities. Together with the data explosion, we are also witnessing a dramatic increase in data processing capabilities, thanks to new powerful parallel computer architectures and more sophisticated algorithms. In this paper we describe the algorithmic design and the optimization techniques that led to the unprecedented processing rate of 15.3 trillion edges per second on 64 thousand Blue Gene/Q nodes, that allowed the in-memory exploration of a petabyte-scale graph in just a few seconds. This paper provides insight into our parallelization and optimization techniques. We believe that these techniques can be successfully applied to a broader class of graph algorithms. © 2014 IEEE.