Document sentences as a small world

In this paper we describe the possibility of constructing the well-known small world topology for an ordinary document, based on the actual document structure. Sentences in such a graph are represented by nodes, which are connected if and only if the corresponding sentences are neighbors or share at least one common keyword. This graph is built using a carefully selected one-parameter set of keywords. By varying this parameter - the level of meaningfulness - we transition the document-representing graph from a trivial path graph into a large random graph. During such a conversion, as the parameter is varied over its range, the graph becomes a small world. This in turn opens the possibility of applying many well-established ranking algorithms to the problem of ranking sentences and paragraphs in text documents. These rankings are, in turn, crucial for document understanding, summarization and information extraction. These graphs can also serve as a source of interesting small world graphs for the theory of complex networks.