We provide here irrefutable facts that prove the falsehood of the claims published in [1] by Dehmer and Mowshowitz (DM) against our paper published in [2]. We first prove that Dehmer’s definition of node probability [3] is flawed. In addition, we show that it was not Dehmer in [3] who proposed this definition for the first time. We continue by proving how the use of Dehmer’s definition does not reveal all the physico-mathematical richness of the walk entropy of graphs. Finally, (...) we show a few facts about the failure of DM themselves to cite properly the relevant literature in their field. We also show here how the Editors of Complexity have failed to manage the publication of [1] in an appropriate way according to the accepted guidelines given in the Code of Conduct and Best Practice Guidelines for Journal Editors, published by the Committee on Publication Ethics (COPE). (shrink)