  A crucial challenge in network theory is the study of the robustness of a
network after facing a sequence of failures. In this work, we propose a
dynamical definition of network's robustness based on Information Theory, that
considers measurements of the structural changes caused by failures of the
network's components. Failures are defined here, as a temporal process defined
in a sequence. The robustness of the network is then evaluated by measuring
dissimilarities between topologies after each time step of the sequence,
providing a dynamical information about the topological damage. We thoroughly
analyze the efficiency of the method in capturing small perturbations by
considering both, the degree and distance distributions. We found the network's
distance distribution more consistent in capturing network structural
deviations, as better reflects the consequences of the failures. Theoretical
examples and real networks are used to study the performance of this
methodology.
