  We study the strategy to optimally maximize the dynamic range of excitable
networks by removing the minimal number of links. A network of excitable
elements can distinguish a broad range of stimulus intensities and has its
dynamic range maximized at criticality. In this study, we formulate the
activation propagation in excitable networks as a message passing process in
which the critical state is reached when the largest eigenvalue of the weighted
non-backtracking (WNB) matrix is exactly one. By considering the impact of
single link removal on the largest eigenvalue, we develop an efficient
algorithm that aims to identify the optimal set of links whose removal will
drive the system to the critical state. Comparisons with other competing
heuristics on both synthetic and real-world networks indicate that the proposed
method can maximize the dynamic range by removing the smallest number of links,
and at the same time maintain the largest size of the giant connected
component.
