We survey extensions to database query languages for retrievals that involve inferencing on the nodes and edges of a graph. Common types of inferencing are to find paths between two nodes, compute a value for a path such as a distance or an elapsed time, and to choose among alternative paths. Applications of graph inferencing are common in data and knowledge engineering applications. Our survey is based on the data model (relational or functional), method of extension (iteration, recursion, or special operators), interface style (string or tabular), and restrictions (data and problem oriented). We examine four languages in detail with different values for these properties: 1) QUEL*, 2) Objected-Oriented Functional Data Language, 3) G-WHIZ, and 4) ALPHA. The characteristics of other languages are summarized in several tables. The results of our survey indicate the diversity of language extensions and the need to provide data model and query language features to reason about such problems.