# A High Robustness and Low Cost Model for Cascading Failures

## TL;DR

This paper proposes a cost-effective method to enhance the robustness of networks against cascading failures by selectively protecting fewer vertices, demonstrated through simulations on scale-free and power grid networks.

## Contribution

Introduces a novel approach to prevent cascading failures by protecting fewer vertices, improving robustness with lower costs.

## Key findings

- Networks can be made more robust with less cost using the proposed method.
- The method is effective on both artificial scale-free networks and real power grid structures.
- Selective vertex protection significantly reduces the risk of cascading failures.

## Abstract

We study numerically the cascading failure problem by using artificially created scale-free networks and the real network structure of the power grid. The capacity for a vertex is assigned as a monotonically increasing function of the load (or the betweenness centrality). Through the use of a simple functional form with two free parameters, revealed is that it is indeed possible to make networks more robust while spending less cost. We suggest that our method to prevent cascade by protecting less vertices is particularly important for the design of more robust real-world networks to cascading failures.