  Percolation, the formation of a macroscopic connected component, is a key
feature in the description of complex networks. The dynamical properties of a
variety of systems can be understood in terms of percolation, including the
robustness of power grids and information networks, the spreading of epidemics
and forest fires, and the stability of gene regulatory networks. Recent studies
have shown that if network edges are added "competitively" in undirected
networks, the onset of percolation is abrupt or "explosive." The unusual
qualitative features of this phase transition have been the subject of much
recent attention. Here we generalize this previously studied network growth
process from undirected networks to directed networks and use finite-size
scaling theory to find several scaling exponents. We find that this process is
also characterized by a very rapid growth in the giant component, but that this
growth is not as sudden as in undirected networks.
