  Boolean networks serve as discrete models of regulation and signaling in
biological cells. Identifying the key controllers of such processes is
important for understanding the dynamical systems and planning further
analysis. Here we quantify the dynamical impact of a node as the probability of
damage spreading after switching the node's state. We find that the leading
eigenvector of the adjacency matrix is a good predictor of dynamical impact in
the case of long-term spreading. This so-called eigenvector centrality is also
a good proxy measure of the influence a node's initial state has on the
attractor the system eventually arrives at. Quality of prediction is further
improved when eigenvector centrality is based on the weighted matrix of
activities rather than the unweighted adjacency matrix. Simulations are
performed with ensembles of random Boolean networks and a Boolean model of
signaling in fibroblasts. The findings are supported by analytic arguments from
a linear approximation of damage spreading.
