Modeling distributions of node characteristics in directed graphs evolving by preferential attachment

Distributions of in-degree and out-degree in directed graphs evolving by the linear preferential attachment (PA) without edge and node deletion were derived in Bollob\'{a}s, Riordan (2002). The same distributions, but in undirected graphs evolving by the PA with edge and node deletion, were obtained in Ghoshal et al. (2013). Our paper is devoted to a modeling of in- and out-degree distributions in directed graphs evolving by the PA and with edge and node deletion. The PA model is taken the same way as in Ghoshal et al. (2013). We show by a simulation study that the in- and out-degree distributions can be modeled by a power-law distribution or a power-law distribution with an exponential correction depending on the PA parameters.