Group Vitality Indices: Axioms and Algorithms

Kucharczuk, Natalia; Skibski, Oskar

doi:10.24963/ijcai.2026/385

Group Vitality Indices: Axioms and Algorithms

Natalia Kucharczuk, Oskar Skibski

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Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence. Main Track. Pages 3461-3469.

https://doi.org/10.24963/ijcai.2026/385

Keywords

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

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.

Natalia Kucharczuk, and Oskar Skibski. 2026. Group Vitality Indices: Axioms and Algorithms. In Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence, IJCAI-26. IJCAI, 3461–3469. https://doi.org/10.24963/ijcai.2026/385

@inproceedings{ijcai2026p385,
  title     = {Group Vitality Indices: Axioms and Algorithms},
  author    = {Kucharczuk, Natalia and Skibski, Oskar},
  booktitle = {Proceedings of the Thirty-Fifth International Joint Conference on
               Artificial Intelligence, {IJCAI-26}},
  publisher = {International Joint Conferences on Artificial Intelligence Organization},
  editor    = {Diego Calvanese},
  pages     = {3461--3469},
  year      = {2026},
  month     = {8},
  note      = {Main Track},
  doi       = {10.24963/ijcai.2026/385},
  url       = {https://doi.org/10.24963/ijcai.2026/385},
}

TY  - CPAPER
TI  - Group Vitality Indices: Axioms and Algorithms
AU  - Kucharczuk, Natalia
AU  - Skibski, Oskar
T2  - Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence, IJCAI-26
PB  - International Joint Conferences on Artificial Intelligence Organization
PY  - 2026
SP  - 3461
EP  - 3469
DO  - 10.24963/ijcai.2026/385
UR  - https://doi.org/10.24963/ijcai.2026/385
ER  -