Redefining research metrics: Introducing the inverse-H-index and efficacy equation in scholarly publication analysis

The exploratory study examines the distribution of scholarly publications and citations within a geometric Graph-H framework, focusing on identifying and addressing gaps in the distribution matrix. Additionally, the paper introduces the economic concept of paper publications. Utilizing the geometric principles foundational to the original H-index, this study proposes the inverse-H-index as a metric to quantify discrepancies between citation counts and optimal capacity. Based on this quantified framework, the paper introduces an efficacy concept and equation to evaluate the effectiveness of researchers in achieving their H-index values through their publications and citations. The validity of this equation is assessed through Pearson testing and validation using datasets from Clarivate's report. By comparing the H-index, inverse-H-index, and efficacy measures across different groups of scholars, this study finds that the proposed equation effectively captures researchers' publication activities and identifies attributes not highlighted by the traditional H-index. • The Inverse-H-Index aims to evaluate the “cost” of the research publications. • Based on the inverse-H-index, the paper introduces Efficacy and an equation. • The Efficacy aims to evaluate the effectiveness of scholars in achieving H-index. • The Inverse-H-index and Efficacy examine gaps in H-index and other impact measures.