Information Theory Perspective on Network Robustness
  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. 
Tiago A. Schieber, Laura Carpi, Alejandro C. Frery, Osvaldo A Rosso,   Panos M. Pardalos and Martin G. Ravetti
physics.soc-ph cond-mat.stat-mech cs.SI