Graph similarity and matching

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (p. 85-88).Measures of graph similarity have a broad array of applications, including comparing chemical structures, navigating complex networks like the World Wide Web, and more recently, analyzing different kinds of biological data. This thesis surveys several different notions of similarity, then focuses on an interesting class of iterative algorithms that use the structural similarity of local neighborhoods to derive pairwise similarity scores between graph elements. We have developed a new similarity measure that uses a linear update to generate both node and edge similarity scores and has desirable convergence properties. This thesis also explores the application of our similarity measure to graph matching. We attempt to correctly position a subgraph GB within a graph GA using a maximum weight matching algorithm applied to the similarity scores between GA and GB. Significant performance improvements are observed when the topological information provided by the similarity measure is combined with additional information about the attributes of the graph elements and their local neighborhoods. Matching results are presented for subgraph matching within randomly-generated graphs; an appendix briefly discusses matching applications in the yeast interactome, a graph representing protein-protein interactions within yeast.by Laura Zager.S.M

Links between Kleinberg's hubs and authorities, correspondence analysis and Markov chains

In this work, we show that Kleinberg's hubs and authorities model is closely related to both correspondence analysis, a well-known multivariate statistical technique, and a particular Markov chain model of navigation through the web. The only difference between correspondence analysis and Kleinberg's method is the use of the average value of the hubs (authorities) scores for computing the authorities (hubs) scores, instead of the sum for Kleinberg's method. We also show that correspondence analysis and our Markov model are related to SALSA, a variant of Kleinberg'smodel