Citation graph, weighted impact factors and performance indices

TL;DR

This paper proposes a novel method to evaluate scientific impact by weighting citations based on the citing authors' achievements, using eigenvector analysis of the citation graph.

Contribution

It introduces a new impact assessment scheme that incorporates author-specific citation weights derived from eigenvector components of the citation network.

Findings

Weighted citation counts provide a more nuanced impact measure.

The method enables calculation of weighted impact factors and Hirsch indices.

Eigenvector-based weighting captures the influence of citing authors' achievements.

Abstract

A scheme of evaluating an impact of a given scientific paper based on importance of papers quoting it is investigated. Introducing a weight of a given citation, dependent on the previous scientific achievements of the author of the citing paper, we define the weighting factor of a given scientist. Technically the weighting factors are defined by the components of the normalized leading eigenvector of the matrix describing the citation graph. The weighting factor of a given scientist, reflecting the scientific output of other researchers quoting his work, allows us to define weighted number of citation of a given paper, weighted impact factor of a journal and weighted Hirsch index of an individual scientist or of an entire scientific institution.