Miuz: measuring the impact of disconnecting a node

TL;DR

Miuz is a new robustness index for complex networks that measures the impact of node removal on network connectivity, showing it can identify more damaging attack strategies than traditional centrality measures.

Contribution

Introduces Miuz, a novel index based on connected component sizes, and demonstrates its effectiveness in assessing network robustness under targeted attacks.

Findings

Miuz outperforms traditional centrality measures in identifying critical nodes.

Attacks based on Miuz cause greater network disconnection with fewer nodes.

Miuz provides a valuable addition to existing robustness metrics.

Abstract

In this article we present Miuz, a robustness index for complex networks. Miuz measures the impact of disconnecting a node from the network while comparing the sizes of the remaining connected components. Strictly speaking, Miuz for a node is defined as the inverse of the size of the largest connected component divided by the sum of the sizes of the remaining ones. We tested our index in attack strategies where the nodes are disconnected in decreasing order of a specified metric. We considered Miuz and other well-known centrality measures such as betweenness, degree , and harmonic centrality. All of these metrics were compared regarding the behavior of the robust-ness (R-index) during the attacks. In an attempt to simulate the internet backbone, the attacks were performed in complex networks with power-law degree distributions (scale-free networks). Preliminary results show that attacks based on disconnecting a few number of nodes Miuz are more dangerous (decreasing the robustness) than the same attacks based on other centrality measures. We believe that Miuz, as well as other measures based on the size of the largest connected component, provides a good addition to other robustness metrics for complex networks.