A quantitative comparison of graph-based models for Internet topology
IEEE/ACM Transactions on Networking (TON)
On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
Analysis of the autonomous system network topology
ACM SIGCOMM Computer Communication Review
On the origin of power laws in Internet topologies
ACM SIGCOMM Computer Communication Review
Network topology generators: degree-based vs. structural
Proceedings of the 2002 conference on Applications, technologies, architectures, and protocols for computer communications
Heuristically Optimized Trade-Offs: A New Paradigm for Power Laws in the Internet
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Random Evolution in Massive Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
BRITE: An Approach to Universal Topology Generation
MASCOTS '01 Proceedings of the Ninth International Symposium in Modeling, Analysis and Simulation of Computer and Telecommunication Systems
Does AS size determine degree in as topology?
ACM SIGCOMM Computer Communication Review - Special issue on wireless extensions to the internet
Foundations and Trends in Web Science
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Recent studies observe that vertex degree in the autonomous systems (AS) graph exhibits a highly variable distribution [14, 21]. The most prominent explanatory model for this phenomenon is the Barabasi-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.