  Empirical evidence has revealed that biological regulatory systems are
controlled by high-level coordination between topology and Boolean rules. In
this study, we study the joint effects of degree and Boolean functions on the
stability of Boolean networks. To elucidate these effects, we focus on i) the
correlation between the sensitivity of Boolean variables and the degree, and
ii) the coupling between canalizing inputs and degree. We find that negatively
correlated sensitivity with respect to local degree enhances the stability of
Boolean networks against external perturbations. We also demonstrate that the
effects of canalizing inputs can be amplified when they coordinate with high
in-degree nodes. Numerical simulations confirm the accuracy of our analytical
predictions at both the node and network levels.
