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Accelerating, hyperaccelerating, and decelerating networks.

Authors
  • Gagen, M J
  • Mattick, J S
Type
Published Article
Journal
Physical Review E
Publisher
American Physical Society (APS)
Publication Date
Jul 01, 2005
Volume
72
Issue
1 Pt 2
Pages
16123–16123
Identifiers
PMID: 16090052
Source
Medline
License
Unknown

Abstract

Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular, biological networks can display a quadratic growth in regulator number with genome size even while remaining sparsely connected. These features are mutually incompatible in standard treatments of network theory which typically require that every new network node possesses at least one connection. To model sparsely connected networks, we generalize existing approaches and add each new node with a probabilistic number of links to generate either accelerating, hyperaccelerating, or even decelerating network statistics in different regimes. Under preferential attachment for example, slowly accelerating networks display stationary scale-free statistics relatively independent of network size while more rapidly accelerating networks display a transition from scale-free to exponential statistics with network growth. Such transitions explain, for instance, the evolutionary record of single-celled organisms which display strict size and complexity limits.

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