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On the Emergence of Highly Variable Distributions in the Autonomous System Topology (2003)
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| Venue: | ACM Computer Communication Review |
| Citations: | 4 - 0 self |
BibTeX
@ARTICLE{Fayed03onthe,
author = {Marwan Fayed and Paul Krapivsky and John W. Byers and Mark Crovella and David Finkel and Sid Redner},
title = {On the Emergence of Highly Variable Distributions in the Autonomous System Topology},
journal = {ACM Computer Communication Review},
year = {2003},
volume = {33},
pages = {41--49}
}
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Abstract
Recent studies observe that vertex degree in the autonomous system (AS) graph exhibits a highly variable distribution [14, 21]. The most prominent explanatory model for this phenomenon is the Barab asi-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 [10]; 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, and show that it 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 out-degree will also show high variability. Moreover, our approach is more flexible than previous work, since the choice of which AS to connect to does not impact high variability, thus can be freely specified. We instantiate such a model with empirically derived estimates of historical growth rates and show that the resulting degree distribution is in good agreement with that of real AS graphs.
Keyphrases
highly variable distribution autonomous system topology high variability b-a model exponential growth link formation good agreement power-law tail size distribution empirical data previous work autonomous system degree distribution historical growth rate new node preferential connectivity meaning prominent explanatory model vertex degree recent study preferential connectivity variable distribution general explanation central feature
