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by Marwan Fayed, Paul Krapivsky, John Byers, Mark Crovella, David Finkel, Sid Redner
ACM Computer Communication Review
http://www.cs.bu.edu/techreports/pdf/2003-005-AS-degree-distribution.pdf
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Abstract:
Recent studies have noted that vertex degree in the autonomous system (AS) graph exhibits a highly variable distribution [15, 22]. The most prominent explanatory model for this phenomenon is the Barabási-Albert (B-A) model [5, 2]. A central feature of the B-A model is preferential connectivity — meaning that the likelihood a new node in a growing graph will connect to an existing node is proportional to the existing node’s degree. In this paper we ask whether a more general explanation than the B-A model, and absent the assumption of preferential connectivity, is consistent with empirical data. We are motivated by two observations: first, AS degree and AS size are highly correlated [11]; and second, highly variable AS size can arise simply through exponential growth. We construct a model incorporating exponential growth in the size of the Internet, and in the number of ASes. We then show via analysis that such a model yields a size distribution exhibiting a power-law tail. In such a model, if an AS’s link formation is roughly proportional to its size, then AS degree will also show high variability. We instantiate such a model with empirically derived estimates of growth rates and show that the resulting degree distribution is in good agreement with that of real AS graphs.
Citations
|
699
|
On power-law relationship of the internet topology
– FALOUTSOS, FALOUTSOS, et al.
- 1999
|
|
632
|
Emergence of scaling in random networks
– BARABÁSI, ALBERT
- 1999
|
|
358
|
Statistical mechanics of complex networks
– Albert, Barabási
- 2002
|
|
337
|
Modeling internet topology
– Calvert, Doar, et al.
- 1997
|
|
222
|
Heuristics for Internet Map Discovery
– Govindan, Tangmunarunkit
- 2000
|
|
169
|
BRITE: An Approach to Universal Topology Generation
– Medina, Lakhina, et al.
- 2001
|
|
163
|
A Quantitative Comparison of Graph-based Models for Internet Topology
– Zegura, Donahoo
- 1997
|
|
124
|
On the origin of power laws in internet topologies
– Medina, Matta, et al.
- 2000
|
|
109
|
On distinguishing between internet power law topology generators
– Bu, Towsley
- 2002
|
|
99
|
Network topology generators: degree-based vs. structural
– Tangmunarunkit, Govindan, et al.
|
|
93
|
Topology of Evolving Networks: Local Events and Universality
– Albert, Barabási
- 2000
|
|
85
|
On a class of skew distribution functions
– Simon
- 1955
|
|
74
|
Towards Capturing Representative AS-Level Internet Topologies
– Chang, Govindan, et al.
- 2002
|
|
71
|
Heuristically optimized trade-offs: A new paradigm for power laws
– Fabrikant, Koutsoupias, et al.
- 2002
|
|
55
|
Random evolution in massive graphs
– Aiello, Chung, et al.
- 2001
|
|
45
|
Networks of scientific papers
– Price, J
- 1965
|
|
39
|
Connectivity of growing random networks
– Krapivsky, Redner, et al.
- 2000
|
|
39
|
Spectral analysis of internet topologies
– Gkantsidis, Mihail, et al.
- 2003
|
|
36
|
A general theory of bibliometric and other cumulative advantage processes
– Price
- 1976
|
|
36
|
Analysis of the autonomous system network topology
– Magoni, Pansiot
- 2001
|
|
26
|
Inferring as-level internet topology from router-level path traces
– Chang, Jamin, et al.
- 2001
|
|
19
|
and Albert-László Barabási. Topology of evolving networks: Local events and universality
– Albert
- 2000
|
|
17
|
Towards an optimization-driven framework for designing and generating realistic Internet topologies
– Alderson, Doyle, et al.
|
|
9
|
Truncation of power law behavior in “scale-free” network models due to information filtering
– Mossa, Barthélémy, et al.
- 2002
|
|
6
|
Degree distributions of growing networks
– Krapivsky, Rodgers, et al.
- 2001
|
|
5
|
On the size distribution of autonomous systems
– Fayed, Krapivsky, et al.
- 2003
|
|
3
|
On generating graphs with prescribed degree sequences for complex network modeling applications
– Mihail, Visnoi
- 2002
|
|
1
|
Truncation of Power Law Behavior in "Scale-Free" Network Models due to Information Filtering
– Mossa, emy, et al.
- 2002
|
