On the Emergence of Highly Variable Distributions in the Autonomous System Topology Marwan Fayed, Paul Krapivsky, John W. Byers, Mark Crovella, David Finkel, Sid Redner 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 si-Albert (B-A) model [5, 2]. A cena tral 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: rst, 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
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On the emergence of highly variable distributions in the autonomous system topology
Fayed, Marwan; Krapivsky, Paul; Byers, John W.; Crovella, Mark; Finkel, David; Redner, Sid
Follow ACM SIGCOMM Computer Communication Review
, Volume 33 (2)
Association for Computing Machinery – Apr 1, 2003
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