Accelerating, hyperaccelerating, and decelerating networks

Gagen, M. J. and Mattick, J. S. (2005) Accelerating, hyperaccelerating, and decelerating networks. Physical Review E, 72 1: .


Author Gagen, M. J.
Mattick, J. S.
Title Accelerating, hyperaccelerating, and decelerating networks
Journal name Physical Review E   Check publisher's open access policy
ISSN 1539-3755
Publication date 2005
Sub-type Article (original research)
DOI 10.1103/PhysRevE.72.016123
Volume 72
Issue 1
Total pages 13
Place of publication College Pk
Publisher American Physical Soc
Collection year 2005
Language eng
Subject C1
239901 Biological Mathematics
780102 Physical sciences
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.
Keyword Physics, Fluids & Plasmas
Physics, Mathematical
Complete Genome Sequence
Complex Networks
Evolution
Growth
Model
Distributions
Duplication
Behavior
Family
Q-Index Code C1

 
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