---
title: "Vitality Indices are Equivalent to Induced Game-Theoretic Centralities"
authors:
  - "Oskar Skibski"
doi: "10.24963/ijcai.2021/56"
url: "https://ijcai.org/proceedings/2021/56"
pdf: "https://ijcai.org/proceedings/2021/0056.pdf"
venue: "Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence"
year: 2021
pages: "398-404"
track: "Main Track"
keywords:
  - "Agent-based and Multi-agent Systems: Economic Paradigms, Auctions and Market-Based Systems"
  - "Agent-based and Multi-agent Systems: Cooperative Games"
  - "Machine Learning Applications: Networks"
---

# Vitality Indices are Equivalent to Induced Game-Theoretic Centralities

Oskar Skibski

*Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence*, pages 398-404. DOI: [10.24963/ijcai.2021/56](https://doi.org/10.24963/ijcai.2021/56)

## Abstract

Vitality indices form a class of centrality measures that assess the importance of a node based on the impact its removal has on the network. To date, theoretical analysis of this class is lacking. In this paper, we show that vitality indices can be characterized using the axiom of Balanced Contributions proposed by Myerson in the coalitional game theory literature. We explore the link between both fields and show an equivalence between vitality indices and induced game theoretic centralities based on the Shapley value. Our characterization allows us to easily determine which known centrality measures are vitality indices.