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Publication and Citation Analysis

5.13 CITATION GENERATIONS

In the past little attention has been paid to different citation and reference
generations. Although admittedly a complex issue, we think that taking
more than one generation into account reveals better the structure of the
network underlying progress in science. In particular, when studying a
publication’s contribution to the evolution of its field or to science in
general, taking only direct citations into account, tells only part of the
story. This has been pointed out in (Hu et al., 2011) where it is explained
how citation generations can be studied from different angles. In this sec-
tion we bring this line of reasoning to the attention of the reader. We
start with the notion of a multiset.

5.13.1 Multisets
The notion of a multiset generalizes the notion of a set (Jouannaud &
Lescanne, 1982). In a multiset an element can occur several times. Hence,
{a,a,b,b,b} may denote a multiset. As it is the case for sets, the order plays
no role in a multiset, hence {a,a,b,b,b} 5 {b,a,b,a,b}. More formally a mul-
tiset may be defined as a couple consisting of a set X, and a function m
from X to the natural numbers, such that m(x) denotes the number of
times x belongs to the multiset. As an example, the multiset {a,a,b,b,b}is
formally denoted as (A,m), where

a-2
A 5 a; bg and m:A-N:
f
b-3
5.13.2 Definition: Citation Generations in a Uni-Directed
Citation Network
By the term uni-directed citation network we mean a citation network which
has the property that if there is a directed link between node A and node
B (in this order), then there is certainly no link between node B and
node A (in that order). Consequently this notion applies to citation net-
works between single articles, but not to a network of journal citations
(at least not in the usual sense).
We consider now a set of publications (the target group), for instance
all articles coauthored by scientist S during a given period of time. This
target group is called generation zero. Publications that cite generation