Page 151 - Becoming Metric Wise

142 Becoming Metric-Wise

zero publications or publications that cite publications citing generation
zero publications and so on, build up higher order forward generations.
These are called forward generations as one goes forward in time, hence
these articles come later. Similarly, publications cited by the target group
build up backward generations. However, there are many ways to define
these other generations. Indeed, besides backward and forward genera-
tions, we have two times two types of definitions, denoted here using the
m
s
m
s
symbols G , G , H , and H . Focusing on forward generations, they are
defined as follows.
The first distinction is between disjoint and possibly overlapping gen-
erations. Beginning with the zero-th generation G 0 5 H 0 we make the
following distinction:
• Generation G n contains all publications that cite at least one genera-
tion G n21 publication and that do not yet belong to G k , k 5 0, .. .,
n 2 1.
• Generation H n contains all publications that cite at least one genera-
tion H n21 publication.
Generations of type G n are disjoint, while generations of type H n usu-
ally are not.
The second distinction is between sets and multisets:
• A generation is a set: an element belongs to it or not, and this exactly
once.
• A generation is a multiset: an element may belong to it several times.
This leads to four definitions of forward generations: Generations
s
of type G, considered as sets, hence denoted as G , and considered as
m
multisets, denoted as G ; generations of type H, considered as sets,
s m
denoted as H , and considered as multisets, denoted as H . We, more-
over, require that if an element belongs more than once to a multiset
then it must be connected to the zero generation through different
paths (this is a specification with respect to Hu et al. (2011)).
Backward generations are defined in a similar way. The difference is
that backward generations are determined by references (cited publica-
tions), while forward generations are determined by citing publica-
tions. Forward generations are indicated by adding a positive index,
m
such as G , n being a positive natural number, while backward genera-
n
s
tions are indicated by a negative whole number, such as H ,where
2n
again n is a positive natural number. Note that the zero generation is
always a set (not a proper multiset) and G 0 5 H 0 .