Directed scale-free graphs

Abstract

We introduce a model for directed scale-free graphs that grow with preferential attachment depending in a natural way on the in- and out-degrees. We show that the resulting in- and out-degree distributions are power laws with different exponents, reproducing observed properties of the worldwide web. We also derive exponents for the distribution of in- (out-) degrees among vertices with fixed out- (in-) degree. We conclude by suggesting a corresponding model with hidden variables.