  We investigate the structural and dynamical properties of the transcriptional
regulatory network of the yeast {\it Saccharomyces cerevisiae} and compare it
with two unbiased ensembles: one obtained by reshuffling the edges and the
other generated by mimicking the transcriptional regulation mechanism within
the cell. Both ensembles reproduce the degree distributions (the first -by
construction- exactly and the second approximately), degree-degree correlations
and the $k$-core structure observed in Yeast. An exceptionally large
dynamically relevant core network found in Yeast in comparison with the second
ensemble points to a strong bias towards a collective organization which is
achieved by subtle modifications in the network's degree distributions. We use
a Boolean model of regulatory dynamics with various classes of update functions
to represent in vivo regulatory interactions. We find that the Yeast's core
network has a qualitatively different behaviour, accommodating on average
multiple attractors unlike typical members of both reference ensembles which
converge to a single dominant attractor. Finally, we investigate the robustness
of the networks and find that the stability depends strongly on the used
function class. The robustness measure is squeezed into a narrower band around
the order-chaos boundary when Boolean inputs are required to be nonredundant on
each node. However, the difference between the reference models and the Yeast's
core is marginal, suggesting that the dynamically stable network elements are
located mostly on the peripherals of the regulatory network. Consistently, the
statistically significant three-node motifs in the dynamical core of Yeast turn
out to be different from and less stable than those found in the full
transcriptional regulatory network.
