Kardashian Index

The Kardashian Index (K-Index), named after Kim Kardashian, is a measure of the discrepancy between a scientist's social media profile and publication record. Proposed in 2014, the measure compares the number of followers a research scientist has on Twitter to the number of citations they have for their peer-reviewed work.
Definition.
The relationship between the number of Twitter followers (formula_1) and the number of citations (formula_2) is described as:
formula_3
The Kardashian Index is thus calculated as:
formula_4
where formula_5 is the actual number of Twitter followers of researcher formula_6 and formula_7 is the number that researcher should have given their citations.
Interpretation.
A high K-index indicates an over-blown scientific fame while a low K-index suggests that a scientist is being undervalued. According to the author, researchers whose K-index > 5 can be considered 'Science Kardashians'.
Criticism.
The K-index suggests that the number of citations of a given scientist is comparable to their scientific value. This assumption has been criticized.
On the other hand, the proposal of the K-Index in itself can be interpreted as a criticism to the assumption that scientists should have a social media impact at all while, in reality, social media footprint has no correlation at all to the scientific quality or scientific impact.