Limits and Trade-Offs of Topological Network Robustness |
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Authors: | Christopher Priester Sebastian Schmitt Tiago P. Peixoto |
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Affiliation: | 1. Institut für Festkörperphysik, Technische Universität Darmstadt, Darmstadt, Germany.; 2. Honda Research Institute Europe GmbH, Offenbach am Main, Germany.; 3. Institut für Theoretische Physik, Universität Bremen, Bremen, Germany.; Universidad de Zarazoga, Spain, |
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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. |
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