We describe a general model of a random graph whose degree sequence obeys a power law. Such laws have recently been observed in graphs associated with the world wide web.
|
1669
|
Authoritative sources in a hyperlinked environment
– Kleinberg
- 1999
|
|
904
|
On the evolution of random graphs
– Erdős, Rényi
- 1961
|
|
829
|
Emergence of scaling in random networks
– Barabasi, Albert
- 1999
|
|
786
|
On power-law relationships of the Internet topology
– Faloutsos, Faloutsos, et al.
- 1999
|
|
781
|
Probability inequalities for sums of bounded random variables
– Hoeffding
- 1963
|
|
387
|
Random Graphs
– Janson, ̷Luczak, et al.
- 2000
|
|
337
|
The small world phenomenon: an algorithmic perspective
– Kleinberg
- 1999
|
|
308
|
Small Worlds: The dynamics of networks between order and randomness
– Watts
- 1998
|
|
233
|
A random graph model for massive graphs
– Aiello, Chung, et al.
- 2000
|
|
143
|
Stochastic models for the web graph
– Kumar, Raghavan, et al.
- 2000
|
|
129
|
A Critical Point for Random Graphs with a Given Degree Sequence,” Random Structures and Algorithms
– Molloy, Reed
- 1995
|
|
115
|
A brief history of generative models for power law and lognormal distributions
– Mitzenmacher
|
|
113
|
Probability inequalities for sums of bounded random variables
– Hoeding
- 1963
|
|
107
|
Representing Web graphs
– Raghavan, Garcia-Molina
- 2003
|
|
101
|
The anatomy of a large scale hypertextual Web search engine
– Brin, Page
- 1998
|
|
87
|
The degree sequence of a scale-free random graph process
– Bollobás, Riordan, et al.
- 2001
|
|
68
|
The size of the giant component of a random graph with a given degree sequence
– Molloy, Reed
- 1998
|
|
55
|
A mathematical theory of evolution based on the conclusions of Dr
– Yule
- 1924
|
|
54
|
Towards compressing Web graphs
– Adler, Mitzenmatcher
- 2001
|
|
44
|
The diameter of a cycle plus a random matching
– Bollobás, Chung
- 1988
|
|
32
|
Graph theory in practice
– Hayes
- 2000
|
|
31
|
Variations on random graph models for the web
– Drinea, Enachescu, et al.
- 2001
|
|
31
|
Problems and Theorems in Analysis I
– P'olya, Szego
- 1970
|
|
31
|
Samukhin, “Structure of Growing Networks with Preferential Linking,” Phys
– Dorogovtsev, Mendes, et al.
- 2000
|
|
28
|
The Calculus of Finite Differences
– Milne-Thomson
- 1965
|
|
28
|
On a Class of Skewed Distribution Functions’, Biometrika 42(3/4
– Simon
- 1955
|
|
26
|
The diameter of the World Wide Web,'' Nature 401
– Albert, Jeong, et al.
- 1999
|
|
25
|
Popularity based random graph models leading to a scale-free degree sequence, preprint available from http://www.informatik.hu-berlin.de/,osthus
– Buckley, Osthus
|
|
16
|
The diameter of the world wide web, Nature
– Albert, Jeong, et al.
- 1999
|
|
11
|
The size of the largest strongly connected component of a random digraph with a given degree sequence, Combinatorics, Probability and Computing 13
– Cooper, Frieze
- 2004
|
|
11
|
Mathematical results on scale-free graphs, Handbook of Graphs and Networks
– Bollob'as, Riordan
- 2002
|
|
10
|
The degree sequence of a scale free random graph process, Random Structures and Algorithms 18
– Bollob'as, Riordan, et al.
- 2001
|
|
8
|
Crawling on web graphs
– Cooper, Frieze
- 2002
|
|
7
|
The diameter of a scale free random graph
– Bollobas, Riordan
|
|
7
|
The Calculus of Finite Dierences
– Milne-Thomson
- 1951
|
|
5
|
Graph Theory in Practice: Part II
– Hayes
- 2000
|
|
5
|
The web as a graph. www.almaden.ibm.com
– Kumar, Raghavan, et al.
|
|
5
|
Stochastic models for the web graph. www.almaden.ibm.com
– Kumar, Raghavan, et al.
|
|
2
|
The degree sequence of a scale free random graph process
– Bollobs, Riotdan, et al.
|
|
2
|
The diameter of a scale free random graph
– Bollobs, Riotdan
|
|
1
|
Directed web graphs
– Kovalenko
|
|
1
|
T.Luczak and A.Ruciiski, Random Graphs
– Janson
- 2000
|
|
1
|
The web as a graph. rw. almadan. ibm. corn
– Kumar, Raghavan, et al.
|
|
1
|
Stochastic models for the web graph. ww. a/maden. ibm. corn
– Kumar, Raghavan, et al.
|
|
1
|
Problems and Theorems in Analysis I
– P61ya, SzegS
- 1970
|
|
1
|
Distribution of vertex degree
– Cooper
- 2002
|
|
