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

D. Fraiman ()

The European Physical Journal B: Condensed Matter and Complex Systems, 2008, vol. 61, issue 3, 377-388

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

Keywords: 05.65.+b Self-organized systems; 89.75.Kd Patterns; 87.23.Ge Dynamics of social systems; 02.50.Cw Probability theory (search for similar items in EconPapers)
Date: 2008
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1140/epjb/e2008-00075-3

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