What is H – index ? ‘H’ stands for Hirsch index as it was proposed by the J.E. Hirsch in 2005. The h-index is defined as the author-level metric that attempts to measure both the productivity and the citation impact of the publication of the scientist or the scholar.
There are two parameters to be considered –
- Quantity – Numbers of papers
- Quality – Number of citations
Basically, H-index is the largest number such that a number of publications have at least the same number of citations. As a useful index to characterize the scientific output of a researcher.
Calculating the H-index –
For example, consider a Researcher has published total 10 papers.
| Research Paper | No. of Citations |
| 1 | 50 |
| 2 | 40 |
| 3 | 33 |
| 4 | 23 |
| 5 | 12 |
| 6 | 11 |
| 7 | 8 |
| 8 | 5 |
| 9 | 1 |
| 10 | 0 |
H-index is always <= total numbers of papers published
For convenience let us arrange the number of citations in decreasing order.
H-index can not be 10, because there must be at least 10 research papers which have 10 or more than 10 citations. Similarly,
H-index can not be 9,
H-index can not be 8,
H-index is 7 as there are 7 research papers having 7 or more than 7 citations.
Example :
Input : Citations = [7, 6, 5, 4, 3]
Output : 4
Explanation : There are 5 papers in total.
Since the researcher has 4 papers with at least 4 citations each
and the remaining one paper has less than 4 citations.
So H-index is 4.
Approach for finding the H – index :
- Sort the citation array in ascending order or descending order.
- Iterate from the lowest paper to the highest paper.
- The remaining papers (result) is the count of papers that satisfy the condition for H-index.
# calculating H-Index def H_index(citations): # sorting in ascending order citations.sort() # iterating over the list for i, cited in enumerate(citations): # finding current result result = len(citations) - i # if result is less than or equal # to cited then return result if result <= cited: return result return 0 # creating the citations citation = [50, 40, 33, 23, 12, 11, 8, 5, 1, 0] # calling the function print(H_index(citation)) |
Output
7
Time Complexity : O(nlogn + n)
Space Complexity : O(1)
Limitations of H – Index :
- Different fields of researchers can have different citation behavior.
- We can not compare two researchers having different field and huge gap of research experience. Experienced researcher will have high H-index as compare to less experienced researcher.
- H-index value depends on the database you are using it may vary for the different platform.
