Cheeger's inequality is the fundamental result in spectral graph theory, which connects a combina- torial property of a graph and an algebraic quantity of its associated matrix. This connection is important in the theory of expander graphs and the theory of random walks, which we will see in later chapters.
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Abstract. The relationship between the isoperimetric constants of a connected finite graph and the first positive eigenvalues of discrete Laplacians is studied.
Cheeger's inequality is perhaps one of the most fundamental inequalities in Discrete optimization, spectral graph theory and the analysis of Markov Chains. It�...
We will give four proofs of the Cheeger inequality which relates the eigenvalues of a graph with various isoperimetric variations of the. Cheeger constant.
Cheeger constant (graph theory) - Wikipedia
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Cheeger Inequalities is the spectral gap of the Laplacian matrix of the graph. The Cheeger inequality is a fundamental result and motivation for spectral graph�...
Feb 24, 2015 � It turns out that Cheeger's inequality also holds in terms of the second smallest eigenvalue of L′G (without the factor d in the denominator,�...
Cheeger inequalities of a graph are given. cO 2003 Elsevier B.V. All rights reserved. Keywords: Discrete Laplacian; Isoperimetric constant; Cheeger inequality.
Cheeger's inequality [4, 5, 1, 2, 6] is a fundamental tool in spectral graph theory. The upper bound states that if λ2 is small, then ϕ(G) is also small, and�...
Jul 22, 2014 � The typical proof of the classical Cheeger inequality uses a certain variational interpretation of λ2 and there is a similar interpretation of λ�...
The Cheeger inequality for directed graphs provides methods for further bounding the rate of convergence. We will define the Laplacian of a graph as a Hermitian�...
