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Some asymptotic properties of duplication graphs
1Keck Graduate Institute of Applied Life Sciences, 535 Watson Drive, Claremont, California 91711, USA. araval@kgi.edu
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 3, 2004
Summary
This study examines graph growth models, finding power-law distributions in all. Duplication-dominated networks show slow convergence to true distributions, suggesting early structure remnants in biological networks.
Area of Science:
- Graph theory
- Network science
- Computational biology
Background:
- Duplication graphs model biological networks like protein-protein interaction and gene regulatory networks.
- Understanding network growth dynamics is crucial for analyzing complex biological systems.
Purpose of the Study:
- To investigate three graph growth models, including pure duplication and two-parameter models.
- To analyze the emergence and properties of power-law degree distributions in these models.
- To explore the characteristics of 'duplication-dominated' regimes within the growth dynamics.
Main Methods:
- Mathematical modeling of graph growth dynamics.
- Analysis of degree distributions in pure duplication and two-parameter models.
- Study of asymptotic properties and scaling exponents in different parameter regimes.
Main Results:
- A power-law degree distribution emerges in all three studied graph growth models.
- In duplication-dominated regimes, the convergence to the asymptotic degree distribution is slow.
- The convergence rate depends on the initial degree distribution, hinting at structural inheritance.
Conclusions:
- Scale-free networks grown in a duplication-dominated manner may retain identifiable features of their initial structure.
- The pure duplication growth model provides insights into the asymptotic properties of these networks.
- Findings suggest a link between early network structure and the emergent properties of biological networks.