Download:
by William Aiello, Fan Chung, Linyuan Lu
Experiment. Math
http://math.ucsd.edu/~fan/power.pdf
Add To MetaCart
Abstract:
We propose a random graph model which is a special case of sparse random graphs with given degree sequences which satisfy a power law. This model involves only a small number of parameters, called logsize and log-log growth rate. These parameters capture some universal characteristics of massive graphs. Furthermore, from these parameters, various properties of the graph can be derived. For example, for certain ranges of the parameters, we will compute the expected distribution of the sizes of the connected components which almost surely occur with high probability. We will illustrate the consistency of our model with the behavior of some massive graphs derived from data in telecommunications. We will also discuss the threshold function, the giant component, and the evolution of random graphs in this model. 1
Citations
|
1289
|
The Probabilistic Method
– Alon, Spencer, et al.
- 1992
|
|
787
|
On the evolution of random graphs
– ERDÖS, A
- 1960
|
|
699
|
On power-law relationship of the internet topology
– FALOUTSOS, FALOUTSOS, et al.
- 1999
|
|
632
|
Emergence of scaling in random networks
– BARABÁSI, ALBERT
- 1999
|
|
207
|
Trawling the Web for emerging cyber-communities
– Kumar, Raghavan, et al.
- 1999
|
|
206
|
A random graph model for massive graphs
– Aiello, Chung, et al.
- 2000
|
|
196
|
The Web as a graph: Measurements, models, and methods
– Kleinberg, Kumar, et al.
- 1999
|
|
134
|
Stochastic models for the web graph
– Kumar, Raghavan, et al.
- 2000
|
|
115
|
Scale-free characteristics of random networks: The topology of the World-Wide Web
– BArabasi, Albert, et al.
- 2000
|
|
102
|
A critical point for random graphs with a given degree sequence, Random Structures and Algorithms
– Molloy, Reed
- 1995
|
|
101
|
Models of random regular graphs
– Wormald
- 1999
|
|
85
|
Extracting large-scale knowledge bases from the web
– Kumar, Raghavan, et al.
- 1999
|
|
76
|
A functional approach to external graph algorithms
– Abello, Bushsbaum, et al.
- 1998
|
|
63
|
The size of the giant component of a random graph with a given degree sequence
– Molloy, Reed
- 1998
|
|
42
|
On the strength of connectedness of random graphs
– Erdos, Renyi
- 1961
|
|
31
|
Graph theory in practice
– Hayes
- 2000
|
|
28
|
The asymptotic connectivity of labeled regular graphs
– Wormald
- 1981
|
|
26
|
Sparse random graphs with a given degree sequence
– ̷Luczak
- 1989
|
|
10
|
personal communication
– Raghavan
|
|
6
|
Random evolution of power law graphs, manuscript
– Aiello, Chung, et al.
|
|
1
|
Random evolution of power law graphs
– Aiello, Chung, et al.
|
