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We compute the stationary in-degree probability, $P_{in}(k)$, for a growingnetwork model with directed edges and arbitrary out-degree probability. Inparticular, under preferential linking, we find that if the nodes have a lighttail (finite variance) out-degree distribution, then the correspondingin-degree one behaves as $k^{-3}$. Moreover, for an out-degree distributionwith a scale invariant tail, $P_{out}(k)\sim k^{-\alpha}$, the correspondingin-degree distribution has exactly the same asymptotic behavior only if$2<\alpha<3$ (infinite variance). Similar results are obtained whenattractiveness is included. We also present some results on descriptivestatistics measures %descriptive statistics such as the correlation between thenumber of in-going links, $D_{in}$, and outgoing links, $D_{out}$, and theconditional expectation of $D_{in}$ given $D_{out}$, and we calculate thesemeasures for the WWW network. Finally, we present an application to thescientific publications network. The results presented here can explain thetail behavior of in/out-degree distribution observed in many real networks.

Growing Networks: Limit in-degree distribution for arbitrary out-degree one