  How the architecture of gene regulatory networks ultimately shapes gene
expression patterns is an open question, which has been approached from a
multitude of angles. The dominant strategy has been to identify non-random
features in these networks and then argue for the function of these features
using mechanistic modelling. Here we establish the foundation of an alternative
approach by studying the correlation of eigenvectors with synthetic gene
expression data simulated with a basic and popular model of gene expression
dynamics -- attractors of Boolean threshold dynamics in signed directed graphs.
  Eigenvectors of the graph Laplacian are known to explain collective dynamical
states (stationary patterns) in Turing dynamics on graphs. In this study, we
show that eigenvectors can also predict collective states (attractors) for a
markedly different type of dynamics, Boolean threshold dynamics, and category
of graphs, signed directed graphs. However, the overall predictive power
depends on details of the network architecture, in a predictable fashion.
  Our results are a set of statistical observations, providing the first
systematic step towards a further theoretical understanding of the role of
eigenvectors in dynamics on graphs.
