Properties of a random attachment growing network

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

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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 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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ASJC Scopus subject areas

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

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