Information Technology Reference
In-Depth Information
Table 2.1.
A list of empirical laws for complex webs is given according to their accepted names in the
disciplines in which they were first developed. The power-law index
α
is different for each of the laws
and is intended to be generic; the value listed is from the original reference and need not be the
accepted value today.
Discipline
Law's name
Form of law
Anthropology
1913 [
4
]
Auerbach
Pr(city size rank
r
)
∝
1
/
r
Pr(intensity
>
I
)
∝
1
/
I
α
1998 [
65
]
War
1978 [
86
]
1/
f
Music
Spectrum(
f
)
∝
1
/
f
Biology
1992 [
87
]
/
f
α
DNA sequence
Symbol spectrum(frequency
f
)
∝
1
Pr(
k
species connections)
∝
1
/
k
1
.
1
2000 [
49
]
Ecological web
Pr(
k
connections)
∝
1
/
k
2
.
4
2001 [
35
]
Protein
/
k
2
.
2
2000 [
34
]
Metabolism
Pr(
k
connections)
∝
1
/
k
α
2001 [
40
]
Sexual relations
Pr(
k
relations)
∝
1
Botany
1883 [
64
]
Branching;
d
0
d
1
d
2
da Vinci
=
+
No. of genera(No. of species
N
)
∝
1
/
N
α
1922 [
101
]
Willis
d
2
.
5
0
d
2
.
5
1
d
2
.
5
2
1927 [
51
]
Murray
=
+
Economics
1897 [
56
]
Pr(income
x
)
∝
1
/
x
1
.
5
Pareto
Pr(stock price variations
x
)
∝
1
/
x
3
1998 [
24
]
Price variations
Geophysics
1894 [
55
]
Omori
Pr(aftershocks in time
t
)
∝
1
/
t
Pr(No. of ore fragments
<
size
r
)
∝
r
α
1933 [
67
]
Rosen-Rammler
/
a
α
Korcak
Pr(island area
A
>
a
)
1938 [
44
]
∝
1
1945 [
31
]
Horton
No. of segments at
n
/No. of segments at
n
+
1
=
constant
x
α
1954 [
26
]
Gutenberg-Richter
Pr(earthquake magnitude
<
x
)
1
/
∝
(basin area)
α
1957 [
27
]
Hack
River length
∝
Length of coastline
∝
1/(ruler size)
α
1977 [
44
]
Richardson
Frequency density(burned area
A
)
∝
1
/
A
1
.
38
2004 [
84
]
Forest fires
Information theory
1999 [
32
]
Pr(
k
connections)
∝
1
/
k
1
.
94
World Wide Web
Pr(
k
connections)
∝
1
/
k
α
1999 [
19
]
Internet
The listing of empirical laws in these tables is not intended to be exhaustive, any more
than are the figures given throughout the topic. The phenomena recorded are merely
representative of the interconnectedness of the phenomena that we have historically
partitioned into the various disciplines of science. What we hope to accomplish through
such listings is to make the reader aware of the multitude of ways in which complex
webs are manifest in phenomena that we read about and talk about every day, from
the frequency of earthquakes around the world to the debate over the causes of global
warming, from the reasons for economic upheaval to the causes of war and how we
