  Estimating the influence that individual nodes have on one another in a
Boolean network is essential to predict and control the system's dynamical
behavior, for example, detecting key therapeutic targets to control pathways in
models of biological signaling and regulation. Exact estimation is generally
not possible due to the fact that the number of configurations that must be
considered grows exponentially with the system size. However, approximate,
scalable methods exist in the literature. These methods can be divided in two
main classes: (i) graph-theoretic methods that rely on representations of
Boolean dynamics into static graphs, (ii) and mean-field approaches that
describe average trajectories of the system but neglect dynamical correlations.
Here, we compare systematically the performance of these state-of-the-art
methods on a large collection of real-world gene regulatory networks. We find
comparable performance across methods. All methods underestimate the ground
truth, with mean-field approaches having a better recall but a worse precision
than graph-theoretic methods. Computationally speaking, graph-theoretic methods
are faster than mean-field ones in sparse networks, but are slower in dense
networks. The preference of which method to use, therefore, depends on a
network's connectivity and the relative importance of recall vs. precision for
the specific application at hand.
