Abstract
Coherence of a network means that it is made up of functions of nodes glued together. In our previous work [Haruna, T., 2013. BioSystems 114, 125-148], we showed that coherence of directed networks can be captured by the lateral path which is dual to the usual directed path. In this paper, we study coherence along lateral paths emerging from random Boolean network dynamics. A stochastic way to walk on a directed network along lateral paths based on sensitivity of random Boolean dynamics is proposed and coherence percolation is introduced. We develop mean-field and semi-mean-field theories for coherence percolation and derive the critical condition. As an application to real-world networks, we show that coherence percolation on the gene regulatory network of a bacterium Escherichia coli can be well-captured by the semi-mean-field theory. For the bacterium gene regulatory network, the coherence criticality precedes the dynamical criticality. We discuss the relationship between coherence of the network and the degree distribution in terms of the dynamical criticality hypothesis of real-world gene regulatory networks.
