A new method of hierarchical clustering of graph vertexes is suggested. In the method, the graph partition is determined with an equivalence relation satisfying a recursive definition stating that vertexes are equivalent if the vertexes they point to (or vertexes pointing to them) are equivalent. Iterative application of the partitioning yields a hierarchical clustering of graph vertexes. The method is applied to the citation graph of hep-th. The outcome is a two-level classification scheme for the subject field presented in hep-th, and indexing of the papers from hep-th in this scheme. A number of tests show that the classification obtained is adequate.
The importance of a Web page is an inherently subjective matter, which depends on the readers interests, knowledge and attitudes. But there is still much that can be said objectively about the relative importance of Web pages. This paper describes PageRank, a mathod for rating Web pages objectively and mechanically, effectively measuring the human interest and attention devoted to them. We compare PageRank to an idealized random Web surfer. We show how to efficiently compute PageRank for large numbers of pages. And, we show how to apply PageRank to search and to user navigation.  The network structure of a hyperlinked environment can be a rich source of information about the content of the environment, provided we have effective means for understanding it. We develop a set of algorithmic tools for extracting information from the link structures of such environments, and report on experiments that demonstrate their effectiveness in a variety of context on the World Wide Web. The central issue we address within our framework is the distillation of broad search topics, through the discovery of “authorative” information sources on such topics. We propose and test an algorithmic formulation of the notion of authority, based on the relationship between a set of relevant authoritative pages and the set of “hub pages” that join them together in the link structure. Our formulation has connections to the eigenvectors of certain matrices associated with the link graph; these connections in turn motivate additional heuristrics for link-based analysis.