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We present pest, a novel approach to the approximate querying of graph-structured data such as RDF that exploits the data's structure to propagate term weights between related data items. We focus on data where meaningful answers are given through the application semantics, e.g., pages in wikis, persons in social networks, or papers in a research network such as Mendeley. The pest matrix generalizes the Google Matrix used in PageRank with a term-weight dependent leap and accommodates different levels of (semantic) closeness for different relations in the data, e.g., friend vs. co-worker in a social network. Its eigenvectors represent the distribution of a term after propagation. The eigenvectors for all terms together form a (vector space) index that takes the structure of the data into account and can be used with standard document retrieval techniques. In extensive experiments including a user study on a real life wiki, we show how pest improves the quality of the ranking over a range of existing ranking approaches, yet achieves a query performance comparable to a plain vector space index.