Algebraic Connectivity of Graphs, with Applications
نویسندگان
چکیده
The analysis of matrices associated with discrete, pairwise comparisons can be a very useful toolbox for a computer scientist. In particular, Spectral Graph Theory is based on the observation that eigenvalues and eigenvectors of these matrices betray a lot of properties of graphs associated with them. The first major section of this paper is a survey of key results in Spectral Graph Theory. There are fascinating results involving the connectivity, spanning trees, and a natural measure of bi-partiteness in graphs. Some common applications include clustering, graph cuts and random walks. In this study, we explore Spectral Graph Theory and possible ways to use these concepts in other areas. One problem that we will address is the Haplotype Phasing problem from Computational Biology, using spectral methods to address certain issues with Clark’s phasing method.
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