Despite the large number of papers on network topology modeling and inference, there still exists ambiguity about the real nature of the Internet AS and router level topology. While recent findings have illustrated the inaccuracies in maps inferred from BGP peering and traceroute measurements, existing topology models still produce static topologies, using simplistic assumptions about power law observations and preferential attachment. Today, topology generators are tightly bound to the observed data used to validate them. Given that the actual properties of the Internet topology are not known, topology generators should strive to reproduce the variability that characterizes the evolution of the Internet topology over time. Future topology generators should be able to express the variations in local connectivity that makes today’s Internet: peering relationships, internal AS topology and routing policies each changing over time due to failures, maintenance, upgrades and business strategies of the network. Topology generators should capture those dimensions, by allowing a certain level of randomness in the outcome, rather than enforcing structural assumptions as the truths about Internet’s evolving structure, which may never be discovered.