In the mathematical field of graph theory the Laplacian matrix, sometimes called admittance matrix or Kirchhoff matrix, is a matrix representation of a graph. Together with Kirchhoff's theorem it can be used to calculate the number of spanning trees for a given graph. The Laplacian matrix can be used to find many other properties of the graph; see spectral graph theory. Cheeger's inequality from Riemannian Geometry has a discrete analogue involving the Laplacian Matrix; this is perhaps the most important theorem in Spectral Graph theory and one of the most useful facts in algorithmic applications. It approximates the sparsest cut of a graph through the second eigenvalue of its Laplacian.
Read more about Laplacian Matrix: Definition, Example, Properties, Deformed Laplacian, Symmetric Normalized Laplacian, Random Walk Normalized Laplacian, As A Matrix Representation of The Negative Discrete Laplace Operator, As An Approximation To The Negative Continuous Laplacian
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