Vulnerability and power on networks

TL;DR

This paper introduces new measures of vulnerability and power in networks inspired by socio-political scenarios, linking them to graph regularizability and using coalition game theory, with computational methods and tests on various networks.

Contribution

It proposes novel vulnerability and power measures at group and node levels, connecting them to graph regularizability and applying coalition game concepts.

Findings

Established a connection between vulnerability and graph regularizability.

Developed computational methods for measuring vulnerability and power.

Validated measures on artificial and real-world networks.

Abstract

Inspired by socio-political scenarios, like dictatorships, in which a minority of people exercise control over a majority of weakly interconnected individuals, we propose vulnerability and power measures defined on groups of actors of networks. We establish an unexpected connection between network vulnerability and graph regularizability. We use the Shapley value of coalition games to introduce fresh notions of vulnerability and power at node level defined in terms of the corresponding measures at group level. We investigate the computational complexity of computing the defined measures, both at group and node levels, and provide effective methods to quantify them. Finally we test vulnerability and power on both artificial and real networks.