Group Vitality Indices: Axioms and Algorithms

Natalia Kucharczuk; Oskar Skibski

IJCAI 20260 citations

Group Vitality Indices: Axioms and Algorithms

Abstract

We consider the problem of assessing a group of nodes in a network. Our focus is on vitality indices—a natural class of centrality measures that evaluate the importance of a node by examining the impact of its removal on the network. We conduct a comprehensive analysis of group vitality indices. Specifically, we show that every vitality index admits a unique extension to groups, which can be defined using a group variant of the Shapley value recently proposed in the literature. We also provide an axiomatization of the entire class, along with two specific group vitality indices that satisfy additional normalization conditions. Furthermore, we study the computational properties of all vitality indices, as well as Group Attachment Centrality.

Game Theory and Economic Paradigms: Cooperative gamesMultidisciplinary Topics and Applications: Web and social networks

BibTeX

@inproceedings{ijcai2026_groupvitalityind,
  title = {Group Vitality Indices: Axioms and Algorithms},
  author = {Natalia Kucharczuk and Oskar Skibski},
  booktitle = {IJCAI 2026},
  year = {2026}
}