Shreim, Berdahl (2008)

Authors: Amer Shreim, Andrew Berdahl, Vishal Sood, Peter Grassberger, and Maya Paczuski
Published in: New Journal of Physics 10, 013028 (January 23, 2008)
More: PDF | arXiv

We apply complex network analysis to the state spaces of random Boolean networks (RBNs). An RBN contains N Boolean elements each with K inputs. A directed state space network (SSN) is constructed by linking each dynamical state, represented as a node, to its temporal successor. We study the heterogeneity of these SSNs at both local and global scales, as well as sample-to-sample fluctuations within an ensemble of SSNs. We use in-degrees of nodes as a local topological measure, and the path diversity (Shreim A et al 2007 Phys. Rev. Lett. 98 198701) of an SSN as a global topological measure. RBNs with 2 ? K ? 5 exhibit non-trivial fluctuations at both local and global scales, while K = 2 exhibits the largest sample-to-sample (possibly non-self-averaging) fluctuations. We interpret the observed ‘multi scale' fluctuations in the SSNs as indicative of the criticality and complexity of K = 2 RBNs. ‘Garden of Eden' (GoE) states are nodes on an SSN that have in-degree zero. While in-degrees of non-GoE nodes for K> 1 SSNs can assume any integer value between 0 and 2^N, for K = 1 all the non-GoE nodes in a given SSN have the same in-degree which is always a power of two.

@article{shreim2008cna,
title={{Complex network analysis of state spaces for random Boolean networks}},
author={Shreim, A. and Berdahl, A. and Sood, V. and Grassberger, P. and Paczuski, M.},
journal={New Journal of Physics},
volume={10},
number={013028},
pages={013028},
year={2008}
}