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    • CAS: Computer Science: Technical Reports
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    •   OpenBU
    • College of Arts and Sciences
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    • CAS: Computer Science: Technical Reports
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    On the Emergence of Highly Variable Distributions in the Autonomous System Topology

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    Date Issued
    2003-03-01
    Author(s)
    Fayed, Marwan
    Krapivsky, Paul
    Byers, John
    Finkel, David
    Redner, Sid
    Crovella, Mark
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    https://hdl.handle.net/2144/1501
    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.
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    • CAS: Computer Science: Technical Reports [585]


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