The effect of euclidean distance in directed scale-free network generation

Krapivsky-Redner model is one of the variations of Barabasi-Albert model a widely known model generating scale- free network. In Krapivsky-Redner model, a directed network whose both in-degree and out-degree distributions follow a power law is created, however; the clustering coefficient is lower than the ones observed in nature. In this paper, we added a new constraint, the Euclidean distance to the attraction formed by popularity. With this new constraint, we preserved the scale-free structure and came up with directed networks with shortened Euclidean edge distance and increased clustering coefficient. We simulated this system within multidimensional spaces ranging from one dimension to five dimensions.