Comments on "Distributed Identification of the Most Critical Node for Average Consensus"

In a previous paper, Liu et al. have presented a distributed method to rank the nodes of a network according to their importance formaintaining a fast average consensus within the network. Their method essentially estimates the decrease in algebraic connectivity for each possible node removal, based on a distributed estimation of the Fiedler vector. In this comment correspondence, we argue that their approach is limited to certain parameter ranges in the average consensus algorithm, and we briefly comment on how the framework can be extended accordingly. We also point out that their proposed algorithm for distributed Fiedler vector computation is essentially a special case of an earlier proposed algorithm, and in fact a numerically unstable version thereof. Finally, we correct some statements in their paper.