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Growing directed networks: stationary in-degree probability for arbitrary out-degree one

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  • D. Fraiman

Abstract

We compute the stationary in-degree probability, P(k in ), 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 in -3 . Moreover, for an out-degree distribution with a scale invariant tail, P(k out )∼k out -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 such as the correlation between the number of in-going links, K in , and outgoing links, K out , and the conditional expectation of K in given K 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. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2008

Suggested Citation

  • D. Fraiman, 2008. "Growing directed networks: stationary in-degree probability for arbitrary out-degree one," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 61(3), pages 377-388, February.
    • Handle: RePEc:spr:eurphb:v:61:y:2008:i:3:p:377-388
    DOI: 10.1140/epjb/e2008-00075-3
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    Cited by:

    1. Daniel Fraiman & Nicolas Fraiman & Ricardo Fraiman, 2017. "Nonparametric statistics of dynamic networks with distinguishable nodes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 546-573, September.

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