GEN02-3: On the Search of Internet AS-level Topology Invariants

There has been a significant amount of work analyzing the Internet AS (Autonomous System)-level topology which gives rise to a number of topology models. Although each of these models is being refined to fit better a particular set of graph properties over time, there is a more fundamental need in knowing the topology invariants. To address this need, we examine how the Internet AS-level topology evolves, using a variety of graph metrics,-a super set of what has been used in recent works. We discover that the AS-level topology shows a clear converging trend only in the normalized Laplacian spectrum (nls). From the theory of nls, we discover further that the converging trend indicates a stabilizing ratio of leaf to core ASes (or customer to provider ASes) on the Internet.