We present a novel algorithm and validation method for disambiguating author names in very large bibliographic data sets and apply it to the full Web of Science (WoS) citation index. Our algorithm relies only upon the author and citation graphs available for the whole period covered by the WoS. A pair-wise publication similarity metric, which is based on common co-authors, self-citations, shared references and citations, is established to perform a two-step agglomerative clustering that first connects individual papers and then merges similar clusters. This parameterized model is optimized using an h-index based recall measure, favoring the correct assignment of well-cited publications, and a name-initials-based precision using WoS metadata and cross-referenced Google Scholar profiles. Despite the use of limited metadata, we reach a recall of 87% and a precision of 88% with a preference for researchers with high h-index values. 47 million articles of WoS can be disambiguated on a single machine in less than a day. We develop an h-index distribution model, confirming that the prediction is in excellent agreement with the empirical data, and yielding insight into the utility of the h-index in real academic ranking scenarios.