Algebraic relationships and centrality measures in citation graphs

Bibliographic Data

ID21442463
AuthorsStergios Tsourekas (International Hellenic University, corresponding author), Antonis Sidiropoulos (0000-0002-3352-0868, International Hellenic University), Georgios Evangelidis (0000-0003-1639-2152, University of Macedonia)
Year2026
Publication date2026-06-22
Peer ReviewedYes
Open AccessYes
TypeARTICLE
VenueScientometrics (JOURNAL)
Journal identifiersISSN: 0138-9130 • E-ISSN: 1588-2861
PublisherSpringer Science and Business Media LLC (PUBLISHER)
DOI10.1007/s11192-026-05686-y
OpenAlexW7165574445
LanguageEN
References cited91

Centrality measures are a common way to describe “importance” in citation graphs, and the literature contains many different approaches. In this article we look at these measures through an algebraic lens, so we can see more clearly how they are built and how they relate to each other. We cover classical measures, spectral methods, random-walk ideas, path-based scores, and learning-based approaches. We also bring in matrix representations, eigenvalue formulations, stochastic operators, graph kernels, higher-order structures, and multilayer extensions. We then discuss a broad set of scientometric indicators, such as the h-index family, prestige-weighted citation metrics, and rankings for journals and venues, and we explain how many of them depend—often implicitly—on algebraic properties of citation graphs. We close with open problems and research directions on temporal modelling, multilayer and higher-order settings, axioms, scalability, interpretability, fairness, and adaptive learning-based centrality. The goal is to offer a clear, structured overview and highlight the main challenges ahead

Algebraic number · Centrality · Citation · Citation analysis · Cover (algebra) · Eigenvalues and eigenvectors · Graph · Set (abstract data type) · Advanced Graph Neural Networks · Complex Network Analysis Techniques · scientometrics and bibliometrics research

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Open DOIOpen Access