Eigenvalues of graphs
نویسنده
چکیده
2 Eigenvalues of graphs 5 2.1 Matrices associated with graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 The largest eigenvalue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.1 Adjacency matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.2 Laplacian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.3 Transition matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 The smallest eigenvalue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 The eigenvalue gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4.1 Expanders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4.2 Edge expansion (conductance) . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4.3 Random walks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.5 The number of different eigenvalues . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.6 Spectra of graphs and optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 18
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تاریخ انتشار 2007