A critical point for random graphs with a given degree sequence
Random Graphs 93 Proceedings of the sixth international seminar on Random graphs and probabilistic methods in combinatorics and computer science
On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
Small worlds: the dynamics of networks between order and randomness
Small worlds: the dynamics of networks between order and randomness
A random graph model for massive graphs
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
On inferring autonomous system relationships in the internet
IEEE/ACM Transactions on Networking (TON)
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 '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Internet connectivity at the AS-level: an optimization-driven modeling approach
MoMeTools '03 Proceedings of the ACM SIGCOMM workshop on Models, methods and tools for reproducible network research
Comparing the Structure of Power-Law Graphs and the Internet AS Graph
ICNP '04 Proceedings of the 12th IEEE International Conference on Network Protocols
DIMES: let the internet measure itself
ACM SIGCOMM Computer Communication Review
iPlane: an information plane for distributed services
OSDI '06 Proceedings of the 7th symposium on Operating systems design and implementation
In search of the elusive ground truth: the internet's as-level connectivity structure
SIGMETRICS '08 Proceedings of the 2008 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
A systematic framework for unearthing the missing links: measurements and impact
NSDI'07 Proceedings of the 4th USENIX conference on Networked systems design & implementation
On the geographic location of Internet resources
IEEE Journal on Selected Areas in Communications
Differentiating complex network models: An engineering perspective
Computers & Mathematics with Applications
Towards a bipartite graph modeling of the internet topology
Computer Networks: The International Journal of Computer and Telecommunications Networking
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In this paper, we seek to understand the intrinsic reasons for the well-known phenomenon of heavy-tailed degree in the Internet AS graph and argue that in contrast to traditional models based on preferential attachment and centralized optimization, the Pareto degree of the Internet can be explained by the evolution of wealth associated with each ISP. The proposed topology model utilizes a simple multiplicative stochastic process that determines each ISP's wealth at different points in time and several "maintenance" rules that keep the degree of each node proportional to its wealth. Actual link formation is determined in a decentralized fashion based on random walks, where each ISP individually decides when and how to increase its degree. Simulations show that the proposed model, which we call Wealth-based Internet Topology (WIT), produces scale-free random graphs with tunable exponent α and high clustering coefficients (between 0.35 and 0.5) that stay invariant as the size of the graph increases. This evolution closely mimics that of the Internet observed since 1997.