Analytical Solution of a Stochastic Content Based Network Model

Details Analytical Solution of a Stochastic Content Based Network Model Analytical Solution of a Stochastic Content Based Network Model

2004-06-25

arxiv.org/abs/q-bio/0406049v2

J. Phys. A: Math. Gen. 38 (2005) 9599--9620

Biology

Quantitative Biology

Molecular Networks

13 pages, 5 figures. Rewrote conclusions regarding the relevance to gene regulation networks, fixed minor errors and replaced

Scientific paper

10.1088/0305-4470/38/44/001

We define and completely solve a content-based directed network whose nodes consist of random words and an adjacency rule involving perfect or approximate matches, for an alphabet with an arbitrary number of letters. The analytic expression for the out-degree distribution shows a crossover from a leading power law behavior to a log-periodic regime bounded by a different power law decay. The leading exponents in the two regions have a weak dependence on the mean word length, and an even weaker dependence on the alphabet size. The in-degree distribution, on the other hand, is much narrower and does not show scaling behavior. The results might be of interest for understanding the emergence of genomic interaction networks, which rely, to a large extent, on mechanisms based on sequence matching, and exhibit similar global features to those found here.

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