Supremacy distribution in evolving networks

Janusz A. Hołyst, Agata Fronczak, and Piotr Fronczak
Phys. Rev. E 70, 046119 – Published 27 October 2004

Abstract

We study a supremacy distribution in evolving Barabasi-Albert networks. The supremacy si of a node i is defined as the total number of all nodes that are not older than i and can be linked to it by a directed path (including the node i). The nodes form a basin connected to the node i as its in-component. For a network with a characteristic parameter m=1,2,3,, the supremacy of an individual node increases with the network age as t(1+m)2 in an appropriate scaling region. It follows that there is a relation s(k)km+1 between a node degree k and its supremacy s, and the supremacy distribution P(s) scales as s12(1+m). Analytic calculations basing on a continuum theory of supremacy evolution and on a corresponding rate equation have been confirmed by numerical simulations.

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  • Received 27 August 2003

DOI:https://doi.org/10.1103/PhysRevE.70.046119

©2004 American Physical Society

Authors & Affiliations

Janusz A. Hołyst*, Agata Fronczak, and Piotr Fronczak

  • Faculty of Physics and Center of Excellence for Complex Systems Research, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland

  • *Electronic address: jholyst@if.pw.edu.pl
  • Electronic address: agatka@if.pw.edu.pl

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Issue

Vol. 70, Iss. 4 — October 2004

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