Releasing anonymized social network data for analysis has been a popular idea among data providers. Despite evidence to the contrary the belief that anonymization will solve the privacy problem in practice refuses to die. This dissertation contributes to the field of social graph de-anonymization by demonstrating that even automated models can be quite successful in breaching the privacy of such datasets. We propose novel machine-learning based techniques to learn the identities of nodes in social graphs, thereby automating manual, heuristic-based attacks. Our work extends the vast literature of social graph de-anonymization attacks by systematizing them. We present a random-forests based classifier which uses structural node features based on neighborhood degree distribution to predict their similarity. Using these simple and efficient features we design versatile and expressive learning models which can learn the de-anonymization task just from a few examples. Our evaluation establishes their efficacy in transforming de-anonymization to a learning problem. The learning is transferable in that the model can be trained to attack one graph when trained on another. Moving on, we demonstrate the versatility and greater applicability of the proposed model by using it to solve the long-standing problem of benchmarking social graph anonymization schemes. Our framework bridges a fundamental research gap by making cheap, quick and automated analysis of anonymization schemes possible, without even requiring their full description. The benchmark is based on comparison of structural information leakage vs. utility preservation. We study the trade-off of anonymity vs. utility for six popular anonymization schemes including those promising k-anonymity. Our analysis shows that none of the schemes are fit for the purpose. Finally, we present an end-to-end social graph de-anonymization attack which uses the proposed machine learning techniques to recover node mappings across intersecting graphs. Our attack enhances the state of art in graph de-anonymization by demonstrating better performance than all the other attacks including those that use seed knowledge. The attack is seedless and heuristic free, which demonstrates the superiority of machine learning techniques as compared to hand-selected parametric attacks.