Page 313 - Becoming Metric Wise

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The Informetric Laws

found in Fairthorne (1969), Yablonsky (1980), and Bookstein (1976,
1979, 1984, 1990).
Egghe, (2005, see Chapter 1: Introduction) describes a large number
of situations in which Lotka’s and Zipf’s law are applied. Zipf’s law is
often illustrated on a log-log scale. The reason is that a power function,
represented on a log-log scale, is seen as a straight line. Indeed, on a log-
B
log scale the function grðÞ 5 , β . 0, becomes
β
r
log gr ðÞ 5 log B 2 β log r (9.13)
Equation (9.13), being of the general form y(x) 5 a 2 bx, represents a
decreasing straight line with slope—β. Examples in terms of Internet
links can be found, e.g., in Adamic and Huberman (2001, 2002) and Lin
(2011).
The ubiquity of these regularities has given rise to several attempts at
explaining them and to corresponding models. The standard explanation
in the field of informetrics is the so-called “Success-Breeds-Success”
principle, also referred to as cumulative advantage, see Simon (1957) and
Price (1976) for the original formulations, and Egghe (2005) for a discus-
sion in the context of Lotkaian informetrics. Cumulative advantage is
related to the Matthew Effect (Merton, 1968, 1988) and goes actually
back to Yule (1925). The Matthew Effect is a socio-psychological phe-
nomenon that got its name from the Gospel according to St. Matthew:

For unto everyone that hath shall be given, and he shall have abundance;
But from him that hath not shall be taken away even that which he hath.
The Matthew Effect as introduced by Merton refers to the habit peo-
ple have of giving credit to already famous people and minimizing or
withholding recognition for scientists who have not (yet) made their
mark.
Assuming exponential growth of sources and items, an explanation has
been proposed by Naranan (1970), see also Egghe (2010d) for a short
proof and the related fractal theory (Egghe, 2005). These explanations
were re-invented in the context of networks by Baraba ´si and Albert
(1999) who refer to it as preferential attachment.
Sometimes there is a so-called King Effect. This expression refers to the
phenomenon where the top one (or two) members of a ranked set show
up as outliers. Such an outlier is then referred to as the Dragon King
(Cerqueti & Ausloos, 2015; Yukalov & Sornette, 2012). This means that
they do not conform to the statistical regularity one observes for the other