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Degree correlation in scale-free graphs

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  • Babak Fotouhi
  • Michael Rabbat

Abstract

We obtain closed form expressions for the expected conditional degree distribution and the joint degree distribution of the linear preferential attachment model for network growth in the steady state. We consider the multiple-destination preferential attachment growth model, where incoming nodes at each timestep attach to β existing nodes, selected by degree-proportional probabilities. By the conditional degree distribution p(ℓ|k), we mean the degree distribution of nodes that are connected to a node of degree k. By the joint degree distribution p(k,ℓ), we mean the proportion of links that connect nodes of degrees k and ℓ. In addition to this growth model, we consider the shifted-linear preferential growth model and solve for the same quantities, as well as a closed form expression for its steady-state degree distribution. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Babak Fotouhi & Michael Rabbat, 2013. "Degree correlation in scale-free graphs," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(12), pages 1-19, December.
    • Handle: RePEc:spr:eurphb:v:86:y:2013:i:12:p:1-19:10.1140/epjb/e2013-40920-6
    DOI: 10.1140/epjb/e2013-40920-6
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    Cited by:

    1. Jose L. Salmeron & Marisol B. Correia & Pedro R. Palos-Sanchez, 2019. "Complexity in Forecasting and Predictive Models," Complexity, Hindawi, vol. 2019, pages 1-3, June.
    2. Giovanni Modanese, 2023. "The Network Bass Model with Behavioral Compartments," Stats, MDPI, vol. 6(2), pages 1-13, March.
    3. Matthew Eden & Rebecca Castonguay & Buyannemekh Munkhbat & Hari Balasubramanian & Chaitra Gopalappa, 2021. "Agent-based evolving network modeling: a new simulation method for modeling low prevalence infectious diseases," Health Care Management Science, Springer, vol. 24(3), pages 623-639, September.
    4. Matteo Smerlak & Brady Stoll & Agam Gupta & James S Magdanz, 2015. "Mapping Systemic Risk: Critical Degree and Failures Distribution in Financial Networks," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-15, July.
    5. Laura Di Lucchio & Giovanni Modanese, 2024. "Generation of Scale-Free Assortative Networks via Newman Rewiring for Simulation of Diffusion Phenomena," Stats, MDPI, vol. 7(1), pages 1-15, February.
    6. M. L. Bertotti & G. Modanese, 2019. "The Bass Diffusion Model on Finite Barabasi-Albert Networks," Complexity, Hindawi, vol. 2019, pages 1-12, April.
    7. Benoit Mahault & Avadh Saxena & Cristiano Nisoli, 2017. "Emergent inequality and self-organized social classes in a network of power and frustration," PLOS ONE, Public Library of Science, vol. 12(2), pages 1-23, February.

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    Keywords

    Statistical and Nonlinear Physics;

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