Properties of a random attachment growing network

Lãszlã Zalãnyi, Gãbor Csãrdi, Tamãs Kiss, Mãté Lengyel, Rebecca Warner, Jan Tobochnik, P. Érdi

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 delta 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 delta, 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 delta and thus in this sense there is no phase transition. However, the average component size diverges for delta> or =1/2.

Original languageEnglish
Article number066104
Pages (from-to)9
Number of pages1
JournalPhysical review. E, Statistical, nonlinear, and soft matter physics
Volume68
Issue number6
DOIs
Publication statusPublished - Dec 1 2003

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Giant Component
Growing Networks
attachment
Phase Transition
Vertex of a graph
Diverge
Structural Properties
Social Networks
Join
Model

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Properties of a random attachment growing network. / Zalãnyi, Lãszlã; Csãrdi, Gãbor; Kiss, Tamãs; Lengyel, Mãté; Warner, Rebecca; Tobochnik, Jan; Érdi, P.

In: Physical review. E, Statistical, nonlinear, and soft matter physics, Vol. 68, No. 6, 066104, 01.12.2003, p. 9.

Research output: Contribution to journalArticle

Zalãnyi, L, Csãrdi, G, Kiss, T, Lengyel, M, Warner, R, Tobochnik, J & Érdi, P 2003, 'Properties of a random attachment growing network', Physical review. E, Statistical, nonlinear, and soft matter physics, vol. 68, no. 6, 066104, pp. 9. https://doi.org/10.1103/PhysRevE.68.066104
Zalãnyi, Lãszlã ; Csãrdi, Gãbor ; Kiss, Tamãs ; Lengyel, Mãté ; Warner, Rebecca ; Tobochnik, Jan ; Érdi, P. / Properties of a random attachment growing network. In: Physical review. E, Statistical, nonlinear, and soft matter physics. 2003 ; Vol. 68, No. 6. pp. 9.
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