As graph representations of data emerge in multiple domains, data analysts need to be able to intelligently select among a magnitude of different data graphs based on the effects different graph operators have on them. Exhaustive execution of an operator over the bulk of available data sources is impractical due to the massive resources it requires. Additionally, the same process would have to be re-implemented whenever a different operator is considered. To address this challenge, this work proposes an efficient graph operator modeling methodology. Our novel approach focuses on the inputs themselves, utilizing graph similarity to infer knowledge about input graphs. The modeled operator is only executed for a small subset of the available graphs and its behavior is approximated for the rest of the graphs using machine learning techniques. Our method is operator-agnostic, as the same similarity information can be reused for modeling multiple graph operators. We also propose a family of similarity measures based on the degree distribution that prove capable of producing high quality estimations, comparable or even surpassing other much more costly, state-of-the-art similarity measures. Our evaluation over both real-world and synthetic graphs indicates that our method achieves extremely accurate modeling of many commonly encountered operators, managing massive speedups over a brute-force alternative.