The Hayastan Shakarian cut: measuring the impact of network disconnections

TL;DR

This paper introduces the Hayastan Shakarian (HS) index, a new robustness measure for complex networks that evaluates the impact of edge disconnections on network connectivity, and demonstrates its effectiveness in attack simulations.

Contribution

The paper presents the HS index as a novel metric for assessing network robustness and compares its effectiveness against existing strategies in simulated attack scenarios.

Findings

HS-based attacks more effectively reduce network robustness

HS index outperforms traditional centrality measures in attack scenarios

Attacks targeting edges with high HS are more damaging to network connectivity

Abstract

In this article we present the Hayastan Shakarian (HS), a robustness index for complex networks. HS measures the impact of a network disconnection (edge) while comparing the sizes of the remaining connected components. Strictly speaking, the Hayastan Shakarian index is defined as edge removal that produces the maximal 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 using the Hayastan Shakarian cut (disconnecting the edge with max HS) and other well-known strategies as the higher betweenness centrality disconnection. All strategies were compared regarding the behavior of the robustness (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 using the Hayastan Shakarian cut are more dangerous (decreasing the robustness) than the same attacks based on other centrality measures. We believe that the Hayastan Shakarian cut, 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.