The Modular Structure of Kauffman Networks

TL;DR

This paper investigates the modular structure of Random Boolean Networks, revealing how relevant elements form clusters that influence the networks' dynamics and phase transition behavior, with implications for biological systems.

Contribution

It introduces the concept of relevant element clusters (modules) and links the phase transition in Boolean Networks to percolation theory, enhancing understanding of network dynamics.

Findings

Relevant element clusters (modules) are key to network dynamics.

Phase transition in Boolean Networks is analogous to percolation transition.

Cluster properties influence attractor scaling in critical networks.

Abstract

This is the second paper of a series of two about the structural properties that influence the asymptotic dynamics of Random Boolean Networks. Here we study the functionally independent clusters in which the relevant elements, introduced and studied in our first paper, are subdivided. We show that the phase transition in Random Boolean Networks can also be described as a percolation transition. The statistical properties of the clusters of relevant elements (that we call modules) give an insight on the scaling behavior of the attractors of the critical networks that, according to Kauffman, have a biological analogy as a model of genetic regulatory systems.