Recently, we have been informed that our publication "A detailed characterization of complex networks using Information Theory" has an important problem that must be considered before calculating the \textbf{Network Fisher Information Measure} for complex networks. Dr. Sang Hoon Lee and Dr. Vinko Zlatic pointed out that, since the quantifier we are proposing for networks consider the node indices to build the random-walk-based distribution, if we permute these indices without altering the network structure, our results for Network Fisher may change. This is, indeed true, and we acknowledge that this is problematic when using our proposal. Nonetheless, we have found an adequate solution that enhances our results for both synthetic and real networks; and does not compromise the initial discussion, only improves it, but it comes with additional computational cost. Thus, as our paper did not address this issue at first, we write you to add the discussion of the dependency of Fisher Information Measure on node indices, and to update the results considering this preprocessing before the calculations.