{"type":"ScholarlyArticle","title":"Group Vitality Indices: Axioms and Algorithms","authors":[{"name":"Natalia Kucharczuk","slug":"natalia-kucharczuk","given":"Natalia","family":"Kucharczuk","affiliation":""},{"name":"Oskar Skibski","slug":"oskar-skibski","given":"Oskar","family":"Skibski","affiliation":""}],"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.","doi":"10.24963/ijcai.2026/385","url":"https://ijcai.org/proceedings/2026/385","pdf":"https://ijcai.org/proceedings/2026/0385.pdf","markdown":"https://ijcai.org/proceedings/2026/385.md","bibtex":"https://ijcai.org/proceedings/2026/bibtex/385","volume":{"slug":"2026","title":"Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2026","url":"https://ijcai.org/proceedings/2026/","year":2026,"location":"Bremen, Germany","dates":"15-21 August 2026","editors":"Diego Calvanese","isbn":"978-1-956792-09-6","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2026"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":385,"pages":{"first":3461,"last":3469},"keywords":["Game Theory and Economic Paradigms: Cooperative games","Multidisciplinary Topics and Applications: Web and social networks"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}