Limits and trade-offs of topological network robustness

TL;DR

This paper explores the fundamental trade-offs in network robustness, revealing that a three-block core-periphery structure optimally balances resistance to random and targeted node removals.

Contribution

It demonstrates that three-block structures are sufficient for optimal robustness trade-offs in large networks, highlighting a common core-periphery pattern.

Findings

Three-block structures are optimal for robustness trade-offs.

A core-periphery structure emerges in Pareto-optimal networks.

Extreme robustness cases correspond to simpler structures.

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.