Power laws and the AS-level internet topology

We study and characterize the topology of the Internet at the autonomous system (AS) level. First, we show that the topology can be described efficiently with power laws. The elegance and simplicity of the power laws provide a novel perspective into the seemingly uncontrolled Internet structure. Second, we show that power laws have appeared consistently over the last five years. We also observe that the power laws hold even in the most recent and more complete topology with correlation coefficient above 99% for the degree-based power law. In addition, we study the evolution of the power-law exponents over the five-year interval and observe a variation for the degree-based power law of less than 10%. Thirdly, we provide relationships between the exponents and other topological metrics.