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Conventional keyword search engines are restricted to a given data model and cannot easily adapt to unstructured, semi-structured or structured data. In this paper, we propose an efficient and adaptive keyword search method, called EASE, for indexing and querying large collections of heterogeneous data. To achieve high efficiency in processing keyword queries, we first model unstructured, semi-structured and structured data as graphs, and then summarize the graphs and construct graph indices instead of using traditional inverted indices. We propose an extended inverted index to facilitate keyword-based search, and present a novel ranking mechanism for enhancing search effectiveness. We have conducted an extensive experimental study using real datasets, and the results show that EASE achieves both high search efficiency and high accuracy, and outperforms the existing approaches significantly.