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Spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated with the graph. Learn about cospectral graphs, Cheeger inequality, Hoffman–Delsarte inequality, and more.
Learn about spectral clustering techniques that use the spectrum of the similarity matrix of the data to perform dimensionality reduction and clustering. Find definitions, algorithms, examples, and applications of spectral clustering in multivariate statistics and image segmentation.
Spectral theory is a branch of mathematics that studies the structure and properties of operators in various spaces. It has applications in physics, quantum mechanics, and harmonic analysis. Learn the definition, history, and examples of spectral theory.
Learn how to define and calculate the Laplacian matrix of a graph, a matrix representation that relates to many useful graph properties. Explore different types of Laplacian matrices, such as symmetric, normalized, and random-walk, and their applications in spectral graph theory and graph signal processing.
Learn about the branch of mathematics that applies algebraic methods to problems about graphs. Explore the three main branches: linear algebra, group theory, and graph invariants.
Learn about the spectral radius of a matrix or a bounded linear operator, which is the maximum of the absolute values of its eigenvalues or spectrum. Find out how to calculate, upper bound, and relate it to the power sequence and graph theory.
An adjacency matrix is a square matrix used to represent a graph, with elements indicating whether pairs of vertices are adjacent or not. Learn about different types of adjacency matrices, their properties, and how they relate to graph theory and spectral graph theory.
Graph partition is the reduction of a graph to a smaller graph by partitioning its nodes into groups. Learn about the applications, complexity and algorithms of graph partition problems, such as bipartition, cut and spectral partitioning.