Scale-free property of directed networks with two intrinsic node weights

This paper proposes a network model to understand the scale-free property of directed networks. The proposed model assigns two intrinsic variables (incoming and outgoing weights) to every node. A directed link is established from node i to node j if the sum of the outgoing weight of node i and the incoming weight of node j exceeds a predetermined threshold. The proposed model allows us to know the exact analytical expressions for degree distributions and clustering. We analytically find that the in-degree and out-degree distributions have power-law tails and their scaling exponents are controllable within the range (1,∞). The average clustering coefficient of nodes with out-degree (or in-degree) n also has a power-law tail as a function of n. We also find that the scaling exponent of the clustering coefficient depends on the correlation between incoming and outgoing weights.