Properties of a random attachment growing network

László Zalányi, Gábor Csárdi, Tamás Kiss, Máté Lengyel, Rebecca Warner, Jan Tobochnik, and Péter Érdi
Phys. Rev. E 68, 066104 – Published 17 December 2003
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Abstract

In this study we introduce and analyze the statistical structural properties of a model of growing networks which may be relevant to social networks. At each step a new node is added which selects k possible partners from the existing network and joins them with probability δ by undirected edges. The “activity” of the node ends here; it will get new partners only if it is selected by a newcomer. The model produces an infinite-order phase transition when a giant component appears at a specific value of δ, which depends on k. The average component size is discontinuous at the transition. In contrast, the network behaves significantly different for k=1. There is no giant component formed for any δ and thus in this sense there is no phase transition. However, the average component size diverges for δ>~12.

  • Received 13 May 2003

DOI:https://doi.org/10.1103/PhysRevE.68.066104

©2003 American Physical Society

Authors & Affiliations

László Zalányi1,2, Gábor Csárdi1,2, Tamás Kiss1,2, Máté Lengyel1,2, Rebecca Warner2,3, Jan Tobochnik2,3,*, and Péter Érdi1,2,3

  • 1Department of Biophysics, KFKI Research Institute for Particle and Nuclear Physics of the Hungarian Academy of Sciences, Budapest, Hungary
  • 2Center for Complex Systems Studies, Kalamazoo College, Kalamazoo, Michigan 49006, USA
  • 3Physics Department, Kalamazoo College, Kalamazoo, Michigan 49006, USA

  • *Corresponding author. Email address: jant@kzoo.edu

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Vol. 68, Iss. 6 — December 2003

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