title: Limits and trade-offs of topological network robustness.
abstract: We investigate the trade-off between the robustness against random and targeted removal of nodes from a network. To this end we utilize the stochastic block model to study ensembles of infinitely large networks with arbitrary large-scale structures. We present results from numerical two-objective optimization simulations for networks with various fixed mean degree and number of blocks. The results provide strong evidence that three different blocks are sufficient to realize the best trade-off between the two measures of robustness, i.e. to obtain the complete front of Pareto-optimal networks. For all values of the mean degree, a characteristic three block structure emerges over large parts of the Pareto-optimal front. This structure can be often characterized as a core-periphery structure, composed of a group of core nodes with high degree connected among themselves and to a periphery of low-degree nodes, in addition to a third group of nodes which is disconnected from the periphery, and weakly connected to the core. Only at both extremes of the Pareto-optimal front, corresponding to maximal robustness against random and targeted node removal, a two-block core-periphery structure or a one-block fully random network are found, respectively.
authors.affiliation: Institut für Festkörperphysik, Technische Universität Darmstadt, Darmstadt, Germany.
authors.forename: Christopher
authors.initials: C
authors.lastname: Priester
authors.affiliation: Honda Research Institute Europe GmbH, Offenbach am Main, Germany.
authors.forename: Sebastian
authors.initials: S
authors.lastname: Schmitt
authors.affiliation: Institut für Theoretische Physik, Universität Bremen, Bremen, Germany.
authors.forename: Tiago P
authors.initials: TP
authors.lastname: Peixoto
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D003491:Cybernetics; D013269:Stochastic Processes