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

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dc.creatorFraiman, Daniel
dc.date2007-04-14
dc.date2007-10-12
dc.date.accessioned2026-07-07T10:11:19Z
dc.date.available2026-07-07T10:11:19Z
dc.descriptionWe 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, $P_{out}(k)\sim k^{-α}$, the corresponding in-degree distribution has exactly the same asymptotic behavior only if $2<α<3$ (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.
dc.description12 pages, 6 figures, v2 adds a section on descriptive statistics, an analisis on www network, typos added
dc.identifierhttps://arxiv.org/abs/0704.1847
dc.identifierhttp://arxiv.org/abs/0704.1847
dc.identifierThe European Physical Journal B 61 3 (2008) 377-388
dc.identifierdoi:10.1140/epjb/e2008-00075-3
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171826
dc.subjectPhysics and Society
dc.subjectData Analysis, Statistics and Probability
dc.titleGrowing Networks: Limit in-degree distribution for arbitrary out-degree one
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