Limits and trade-offs of topological network robustness

PLoS One. 2014 Sep 24;9(9):e108215. doi: 10.1371/journal.pone.0108215. eCollection 2014.

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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Algorithms*
  • Computer Simulation
  • Cybernetics
  • Stochastic Processes

Grants and funding

TPP was funded by the University of Bremen, zentrale Forschunsförderung Linie 04. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Honda Research Institute Europe GmbH provided support in the form of salaries for authors CP and SS, but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The specific roles of these authors are articulated in the ‘author contributions’ section.