Lecture 12 : Introduction to Spectral Graph Theory , Cheeger ’ s inequality
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چکیده
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal publications. Spectral graph theory seeks to relate the eigenvectors and eigenvalues of matrices corresponding to a Graph to the combinatorial properties of the graph. While generally the theorems are designed for unweighted and undirected graphs they can be extended to the weighted graph case and (less commonly) the directed graph case. In these notes we only study undirected graphs. Given a graph G we use A to denote adjacency matrix of the graph and D to denote the diagonal degree matrix of the vertex degrees. Recall these are defined as
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