This paper presents a statistically sound method for measuring the accuracy with which a probabilistic model reflects the growth of a network, and a method for optimising parameters in such a model. The technique is data-driven, and can be used for the modeling and simulation of any kind of evolving network. The overall framework, a Framework for Evolving Topology Analysis (FETA), is tested on data sets collected from the Internet AS-level topology, social networking websites and a co-authorship network. Statistical models of the growth of these networks are produced and tested using a likelihood-based method. The models are then used to generate artificial topologies with the same statistical properties as the originals. This work can be used to predict future growth patterns for a known network, or to generate artificial models of graph topology evolution for simulation purposes. Particular application examples include strategic network planning, user profiling in social networks or infrastructure deployment in managed overlay-based services.