The k-step h-index in citation networks at the paper, author, and institution levels.

• By incorporating higher generations of citation information, the k-step h-index provides a comprehensive assessment of scholarly influence at multiple levels. • The k-step h-indices exhibit strong alignment with measures of novelty and disruption, validating their consistency and potential for capturing innovative contributions. • The k-step h-indices outperform certain benchmarks in accurately ranking expert-selected items, such as milestone papers, distinguished authors, and prestigious institutions. • Higher k-step h-indices demonstrate superior performance compared to lower ones and alternative metrics, showcasing their predictive power in identifying prominent scientific entities. The evaluation of scientific impact plays a crucial role in assessing research contributions. In this study, we introduce the concept of the k-step h-index and investigate its applicability in citation networks at different levels, including papers, authors, and institutions. By incorporating higher generations of citation information, the k-step h-index provides a comprehensive and nuanced measure of scientific influence. It demonstrates exponential growth in k-step citations, capturing valuable information from the Hirsch core and tail. Through power law distribution analysis, we uncover the presence of highly influential entities coexisting with less influential ones, revealing the heterogeneity of impact within citation networks. To validate the effectiveness of the k-step h-index , we utilize a vast dataset from APS, conducting a thorough examination of its consistency and convergent validity. Our findings demonstrate strong correlations between the k-step h-index and conventional metrics, as well as alignment with measures of innovation. This confirms the reliability of the k-step h-index and its ability to capture innovative contributions. Notably, when compared to benchmarks, the k-step h-index outperforms in accurately ranking expert-selected items, including milestone papers, distinguished authors, and prestigious institutions. Higher values of the k-step h-index consistently exhibit superior performance, showcasing their predictive power in identifying prominent scientific entities. These findings hold significant implications for research evaluation, policy-making, and strategic planning, as they pave the way for a more holistic understanding of scholarly contributions. [ABSTRACT FROM AUTHOR]