Whenever librarians use Semantic Web services and standards for representing data, they also generate graphs, whether they intend to or not. Graphs are a new data model for libraries and librarians, and they present new opportunities for library services. In this paper we introduce graph theory and explore its real and potential applications in the context of digital libraries. Part 1 describes basic concepts in graph theory and how graph theory has been applied by information retrieval systems such as Google. Part 2 discusses practical applications of graph theory in digital library environments. Some of the applications have been prototyped at the Los Alamos National Laboratory Research Library, others have been described in peer-reviewed journals, and still others are speculative in nature. The paper is intended to serve as a high-level tutorial to graphs in libraries.

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