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Effects of preference for attachment to low-degree nodes on the degree distributions of a growing directed network and a simple food-web model.

Authors
  • Sevim, Volkan
  • Rikvold, Per Arne
Type
Published Article
Journal
Physical Review E
Publisher
American Physical Society
Publication Date
April 2006
Volume
73
Issue
5 Pt 2
Pages
56115–56115
Identifiers
PMID: 16803006
Source
Medline
License
Unknown

Abstract

We study the growth of a directed network, in which the growth is constrained by the cost of adding links to the existing nodes. We propose a preferential-attachment scheme, in which a new node attaches to an existing node i with probability II(k(i)) approximately k(-1), where k(i) is the number of outgoing links at i. We calculate the degree distribution for the outgoing links in the asymptotic regime t --> infinity, n(k) both analytically and by Monte Carlo simulations. The distribution decays like kmu(k)/Tau(k) for large k, where is a constant. We investigate the effect of this preferential-attachment scheme, by comparing the results to an equivalent growth model with a degree-independent probability of attachment, which gives an exponential outdegree distribution. Also, we relate this mechanism to simple food-web models by implementing it in the cascade model. We show that the low-degree preferential-attachment mechanism breaks the symmetry between in- and outdegree distributions in the cascade model. It also causes a faster decay in the tails of the outdegree distributions for both our network growth model and the cascade model.

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