Probing the h-core: an investigation of the tail–core ratio for rank distributions

• Published in: Scientometrics Vol. 84; no. 2; pp. 431 - 439
• Main Authors: Ye, Fred Y., Rousseau, Ronald
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01-08-2010
• Subjects: Citation analysis; Citation indexes; Computer Science; Information Storage and Retrieval; Library Science; Scholarly publishing; Index; Tail–core ratio; Tail; Core
• ISSN: 0138-9130; 1588-2861
• DOI: 10.1007/s11192-009-0099-6

The set of citations received by a set of publications consists of citations received by articles in the
h
-core and citations received by articles in the
h
-tail. Denoting the cardinalities of these fours sets as
C
,
P
,
C
H
and
C
T
we introduce the tail-core ratio (
C
T
/
C
H
) and show that in practical cases this ratio tends to increase. Introducing further the
k
-index, defined as
k
= (
C
/
P
)/(
C
T
/
C
H
), we show that this index decreases in most practical cases. A power law model is in accordance with these practical observations.