Citation Swing Factor: An Indicator to Measure the Diffusion of Cited Items

Abstract

The h-index, introduced by Hirsch, is based on the mutual variation between the number of cited and source items. The temporally continuous nature of the citation accretion process causes a shift of cited items from the h-core zone to the adjacent citation-asymmetric zones, viz. h-excess zone, or h-tail zone. The name given to this shifting phenomenon is the Diffusion of Cited Items (DCI). In this paper, two new variables are introduced, i.e., the Fold of Excess citation over Total citations (FET), denoted by ε 2 and the Fold of h-core citation over Excess citations (FHE), denoted by θ 2 . On the basis of θ and ε, another indicator is introduced, i.e., the Citation Swing Factor (CSF), defined as , which indicates the differential coefficient of θ with respect to ε. The time dependence of FET and FHE is also discussed. The possible solutions of are derived here. The functionality of CSF ( ) to measure the diffusion process quantitatively will be tested later on for journals, authors and institutions.

An Interpretation of h, e and R indices from the Viewpoint of Riemann Zeta Function

“…2007) and g-index , et al Despite the effectiveness and simplicity, there are some demerits of h index, for instance, the loss of citation information and low resolution. There are many papers describing advantages, disadvantages and possible areas of applications of h-index as discussed by Dutta, (2020). Wu (2010) and Kosmulski (2009) introduced two h-type indices, viz.…”

Citation Trend of Indian Physics and Astronomy Research during 2005 2020 through the Lens of Some New Indicators

“…This paper has calculated and analytically interpreted four indicators (CSF, TC, CU & TU) for 15 core Indian physics and astronomy journals. The indicator CSF has recently been formulated 39 and other three indicators are introduced here.…”

“…This continuous shifting process of the cited-items from Tail zone to Excess zone via the Core zone portrays the diffusion of cited items. The indicator Citation Swing Factor (CSF) has been developed to measure this diffusion process quantitatively 39 .…”

“…Here both θ and ε are continuous variables. The differentiation of θ with respect to ε yielded the value ( ) 39 , where T, H and E indicate total citations, h-core citations and excess citations respectively. The indicator CSF thus points out the shift of h-core citations with respect to fold of excess citations to total citations, which in turn, figures the citation shift from h-core to h-excess zone.…”