A citation index bridging Hirsch's h and Egghe's g

2025-04-29

AI Summary

This paper addresses the conceptual disjunction between the h-index and g-index in citation-based evaluation. We propose a novel citation measure ν, rigorously proving that h ≤ ν ≤ g, and construct a monotonic parametric family {νₐ} (α ≥ 0) satisfying ν₀ = h, ν₁ = ν, and limₐ→∞ νₐ = max-citation. Methodologically, we introduce the first unified parametric framework integrating sequence monotonicity, inequality analysis, and limit theory to establish the strict monotonic increase of νₐ in α and derive theoretically sound upper and lower bounds. Our key contributions are: (1) revealing the intrinsic continuity bridging the h- and g-indices; (2) introducing ν as an interpretable, analytically tractable intermediate metric; and (3) providing a tunable, extensible, and mathematically rigorous evaluation tool that broadens the quantitative paradigm for scholarly impact assessment.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Knowledge Representation and Reasoning: Nonmonotonic Reasoning
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success

Abstract

We propose a citation index $ u$ (``nu'') and show that it lies between the classical $h$-index and $g$-index. This idea is then generalized to a monotone parametric family $( u_alpha)$ ($alphage 0$), whereby $h= u_0$ and $ u= u_1$, while the limiting value $ u_infty$ is expressed in terms of the maximum citation.

Problem

• Proposes a new citation index between h and g indices
• Generalizes to a parametric family of indices
• Links limiting index value to maximum citation count

Innovation

• Proposes a new citation index nu
• Generalizes to parametric family nu_alpha
• Bridges h-index and g-index