# Minimizing the effective graph resistance by adding links is NP-hard

## TL;DR

This paper proves that optimizing the effective graph resistance of a network by adding a limited number of links is an NP-hard problem, highlighting its computational complexity.

## Contribution

It establishes the NP-hardness of minimizing effective graph resistance through link addition, a key insight for network robustness optimization.

## Key findings

- Proves the NP-hardness of the problem.
- Highlights computational challenges in network design.
- Provides theoretical foundation for future algorithms.

## Abstract

The effective graph resistance, also known as the Kirchhoff index, is metric that is used to quantify the robustness of a network. We show that the optimisation problem of minimizing the effective graph resistance of a graph by adding a fixed number of links, is NP-hard.