Degree Distributions of Growing Networks

The in-degree and out-degree distributions of a growing network model are determined. The in-degree is the number of incoming links to a given node (and vice versa for out-degree). The network is built by (i) creation of new nodes which each immediately attach to a preexisting node, and (ii) creation of new links between preexisting nodes. This process naturally generates correlated in-degree and out-degree distributions. When the node and link creation rates are linear functions of node degree, these distributions exhibit distinct power-law forms. By tuning the parameters in these rates to reasonable values, exponents which agree with those of the web graph are obtained.