Page 246 - Becoming Metric Wise

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Indicators

articles. This is yet another number associated to ER(A) (Hu et al., 2012).
In this wayweobtainanother ranked list and wecan determinea
reference-reference index, RR(A), defined as

0
R ðAÞ
RRðAÞ 5 1 2 (7.20)
TRef ðAÞ 1 1
0
where R (A) is the rank of A in the list determined by the number of
references. This approach uses references of references, hence two genera-
tions of references as mentioned in Chapter 5, Publication and Citation
Analysis.
Next we consider all articles that cite A and denote this set as Cit(A).
The number of elements in Cit(A) is denoted as TCit(A). This means
that, taking A’s point of view, we now follow the “is cited by” relation.
Article A and all citing articles form a set, denoted as EC(A) 5 Cit(A) ,
{A}. Again we will attach a positive number to each element of EC(A),
leading to a ranking of the elements of EC(A). As was the case for the
“cites” relation, a number between zero and one will be used to charac-
terize the relative position of A in this ranked list.
First we determine for each element in EC(A) the number of articles
by which it is cited. Next we rank each element in EC(A) according to
its number of received citations. Finally the position of A in this list is
characterized by its citation-citation number

R}ðAÞ
CCðAÞ 5 1 2 (7.21)
TCitðAÞ 1 1
where Rv(A) denotes the rank of A in this new list. Again an average rank
is used in the case of ties. Finally, instead of considering the number of cita-
tions received by each element in EC(A) we can also take the number of
references in each of these articles. In this way we obtain another ranked
list and determine a reference-citation index RC(A)using therelation

RwðAÞ
RCðAÞ 5 1 2 (7.22)
TCitðAÞ 1 1
where Rw(A) is the rank of A in the list determined by the number of
references. Articles that are cited by an article citing A form the set of all
articles which are cocited with A. The meaning of these indicators has
been discussed in (Hu et al., 2012).
We recall that the number of elements in Ref(A) and in EC(A)is
fixed, while the number of elements in Cit(A) and EC(A) may—and