1. A random growth model with any real or theoretical degree distribution
- Author
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Frédéric Giroire, Stéphane Pérennes, Thibaud Trolliet, Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA), Combinatorics, Optimization and Algorithms for Telecommunications (COATI), COMmunications, Réseaux, systèmes Embarqués et Distribués (Laboratoire I3S - COMRED), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), This work has been supported by the French government through the UCA JEDI(ANR-15-IDEX-01) and EUR DS4H (ANR-17-EURE-004) Investments in the Futureprojects, by the SNIF project, and by Inria associated team EfDyNet., ANR-15-IDEX-0001,UCA JEDI,Idex UCA JEDI(2015), Université Nice Sophia Antipolis (1965 - 2019) (UNS), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-COMmunications, Réseaux, systèmes Embarqués et Distribués (Laboratoire I3S - COMRED), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), EfdyNet, SNIF, and ANR-17-EURE-0004,UCA DS4H,UCA Systèmes Numériques pour l'Homme(2017)
- Subjects
FOS: Computer and information sciences ,Random Growth Model ,General Computer Science ,Twitter ,02 engineering and technology ,Poisson distribution ,Preferential attachment ,Power law ,Complex Networks ,[INFO.INFO-SI]Computer Science [cs]/Social and Information Networks [cs.SI] ,Theoretical Computer Science ,[INFO.INFO-NI]Computer Science [cs]/Networking and Internet Architecture [cs.NI] ,symbols.namesake ,Random Graphs ,020204 information systems ,0202 electrical engineering, electronic engineering, information engineering ,Statistical physics ,Mathematics ,Social and Information Networks (cs.SI) ,Degree (graph theory) ,Preferential Attachment ,Computer Science - Social and Information Networks ,Function (mathematics) ,Complex network ,Heavy-Tailed Distributions ,Degree distribution ,Degree Distribution ,[MATH.MATH-PR]Mathematics [math]/Probability [math.PR] ,symbols ,020201 artificial intelligence & image processing ,Node (circuits) - Abstract
The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree distribution. The degree distribution can either be theoretical or extracted from a real-world network. The main idea is to invert the recurrence equation commonly used to compute the degree distribution in order to find a convenient attachment function for node connections - commonly chosen as linear. We compute this attachment function for some classical distributions, as the power-law, broken power-law, geometric and Poisson distributions. We also use the model on an undirected version of the Twitter network, for which the degree distribution has an unusual shape. We finally show that the divergence of chosen attachment functions is heavily links to the heavy-tailed property of the obtained degree distributions., Comment: 23 pages, 3 figures
- Published
- 2023