Content based network model with duplication and divergence

Abstract

We construct a minimal content-based realization of the duplication and divergence model of genomic networks introduced by Wagner [A. Wagner, Proc. Natl. Acad. Sci. {\bf 91}, 4387 (1994)] and investigate the scaling properties of the directed degree distribution and clustering coefficient. We find that the content based network exhibits crossover between two scaling regimes, with log-periodic oscillations for large degrees. These features are not present in the original gene duplication model, but inherent in the content based model of Balcan and Erzan. The scaling exponents ${\gamma }_1$ and ${\gamma }_2={\gamma }_1-1/2$ of the Balcan-Erzan model turn out to be robust under duplication and point mutations, but get modified in the presence of splitting and merging of strings. The clustering coefficient as a function of the degree, $C(d)$, is found, for the Balcan-Erzan model, to behave in a way qualitatively similar to the out-degree distribution, however with a very small exponent ${\alpha }_1=1-{\gamma }_1$ and an envelope for the oscillatory part, which is essentially flat, thus ${\alpha }_2=0$. Under duplication and mutations including splitting and merging of strings, $C(d)$ is found to decay exponentially.

arXiv comment12 pages, 6 figures

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Cited by in corpus (2)

• Analytical Solution of a Stochastic Content Based Network Model
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