2007/04/30 by Daniel Fraiman
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Stochastic processes and statistical mechanics #physics.data-an #physics.soc-ph
paper · pdf · doi:10.1140/epjb/e2008-00075-3
published as The European Physical Journal B 61 3 (2008) 377-388 · 12 pages, 6 figures, v2 adds a section on descriptive statistics, an analisis on www network, typos added
arxiv created 2007/10/12 · openalex publication_date 2008/02/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
We compute the stationary in-degree probability, Pin(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, Pout(k)∼ 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, Din, and outgoing links, Dout, and the conditional expectation of Din given Dout, 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.