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

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

2007-04-14

arxiv.org/abs/0704.1847v2

The European Physical Journal B 61 3 (2008) 377-388

Physics

Physics and Society

12 pages, 6 figures, v2 adds a section on descriptive statistics, an analisis on www network, typos added

Scientific paper

10.1140/epjb/e2008-00075-3

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

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