We give a common description of Simon, Barab'asi--Albert, II-PA and Price growth models, by introducing suitable random graph processes with preferential attachment mechanisms. Through the II-PA model, we prove the conditions for which the asymptotic degree distribution of the Barab'asi--Albert model coincides with the asymptotic in-degree distribution of the Simon model. Furthermore, we show that when the number of vertices in the Simon model (with parameter $alpha$) goes to infinity, a portion of them behave as a Yule model with parameters $(lambda,eta) = (1-alpha,1)$, and through this relation we explain why asymptotic properties of a random vertex in Simon model, coincide with the asymptotic properties of a random genus in Yule model. As a by-product of our analysis, we prove the explicit expression of the in-degree distribution for the II-PA model, given without proof in cite{Newman2005}. References to traditional and recent applications of the these models are also discussed.

Random Graphs Associated to some Discrete and Continuous Time Preferential Attachment Models

PACHON PINZON, Angelica Yohana;POLITO, Federico;SACERDOTE, Laura Lea
2016

Abstract

We give a common description of Simon, Barab'asi--Albert, II-PA and Price growth models, by introducing suitable random graph processes with preferential attachment mechanisms. Through the II-PA model, we prove the conditions for which the asymptotic degree distribution of the Barab'asi--Albert model coincides with the asymptotic in-degree distribution of the Simon model. Furthermore, we show that when the number of vertices in the Simon model (with parameter $alpha$) goes to infinity, a portion of them behave as a Yule model with parameters $(lambda,eta) = (1-alpha,1)$, and through this relation we explain why asymptotic properties of a random vertex in Simon model, coincide with the asymptotic properties of a random genus in Yule model. As a by-product of our analysis, we prove the explicit expression of the in-degree distribution for the II-PA model, given without proof in cite{Newman2005}. References to traditional and recent applications of the these models are also discussed.
162
6
1608
1638
http://arxiv.org/pdf/1503.06150
http://arxiv.org/abs/1503.06150
Preferential attachment, Random graph growth, Discrete and continuous time models, Stochastic processes
Pachon, Angelica; Polito, Federico; Sacerdote, Laura
File in questo prodotto:
File Dimensione Formato  
published.pdf

Accesso riservato

Descrizione: articolo
Tipo di file: PDF EDITORIALE
Dimensione 736.64 kB
Formato Adobe PDF
736.64 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/1551766
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 13
  • ???jsp.display-item.citation.isi??? 13
social impact