Evolutionary Biological Data Science Laboratory

history h-index

The history h-index (Randić 2009) is another metric designed to help distinguish among researchers with identical h-index. It is based on the idea of exploring a power expansion of the citation counts for publications in the core. This index starts by creating a vector representing larger power expansions of citation counts. The k^th element of the vector is the largest rank (i), for which the number of citations for that publication is equal or larger than the rank times 2^k, or

$$H^k=\underset{i}{\max}\left(C_i \geq i \times 2^k\right).$$

By definition, the first (zeroth) entry is h (since 2⁰ = 1). Graphically, this is looking at the intersection (rounding the rank down to the nearest integer) of the citation curve with a series of lines with ever increasing slopes of 2^k: 1 (=h), 2, 4, 8, etc., with the largest k equal to the line with the largest slope that actually intersects the citation curve.

The history h-index is simply the sum of the values in this vector, or

$$H=\sum\limits_{k=0}^{K}{H^k},$$

where K is the largest power of 2 for which C_max >= 2^K.

Example

Publications are ordered by number of citations, from highest to lowest.

	Citations (Ci)	Rank (i)	20	21	22	23	24	25	26
H4 = 1, H5 = 1	57	1	1	2	4	8	16	32	64
H3 = 2	26	2	2	4	8	16	32	64	128
H2 = 3	16	3	3	6	12	24	48	96	192
	12	4	4	8	16	32	64	128	256
H1 = 5	11	5	5	10	20	40	80	160	320
H0 = 6	10	6	6	12	24	48	96	192	384
	4	7	7	14	28	56	112	224	448
	3	8	8	16	32	64	128	256	512
	2	9	9	18	36	72	144	288	576
	1	10	10	20	40	80	160	320	640
	1	11	11	22	44	88	176	352	704
	1	12	12	24	48	96	192	384	768
	1	13	13	26	52	104	208	416	832
	0	14	14	28	56	112	224	448	896
	0	15	15	30	60	120	240	480	960
	0	16	16	32	64	128	256	512	1024
	0	17	17	34	68	136	272	544	1088
	0	18	18	36	72	144	288	576	1152

The sum of all of the H^k values is 18.

History