Evolutionary Biological Data Science Laboratory

career years h-index by diffusion speed

The career years h-index by diffusion speed (Mahbuba and Rousseau 2013) is similar to the career years h-index by average citations per year, but rescales the citation counts per year for the time ellapsed since the year of publication. One could also calculate it for a fixed time window, but here we are using career length at the time of calcuation. One creates a list of years ranked by diffusion speed estimated for all citations for all publications from that year. This list is then processed in the same manner as a typical h-type index, namely the career years h-index by diffusion speed is the largest value h for which at least h years have a diffusion speed of h.

$$\text{career years }h\text{ by diffusion speed}=\underset{i}{\max}\left(i\leq \frac{C_i}{A_i}\right).$$

Because the diffusion speed will often not be an integer, the authors recommend interpolating between this and the next largest value, as with the real h-index, in order to more accurately estimate the metric.

$$h_{int}=\frac{\left(h+1\right)\frac{C_h}{A_h}-h\frac{C_{h+1}}{A_{h+1}}}{1-\frac{C_{h+1}}{A_{h+1}}+\frac{C_h}{A_h}}.$$

Example

Years are ordered by diffusion speed per year, from highest to lowest.

Year (yi)	1997	2000	1998	2001	1999
Age (Ai)	5	2	4	1	3
Citations (Ci)	107	16	16	2	4
Diffusion Speed (Ci/Ai)	21.40	8.00	4.00	2.00	1.33
Rank (i)	1	2	3	4	5
			h = 3

The largest rank where i ≤ C_i/A_i is 3. The interpolated rank betweeen this and the next largest value is 3.33.

History