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We prove Cheeger inequalities for p-Laplacians on finite and infinite weighted graphs.
Pointwise estimates and quasilinear parabolic equations
N.S. Trudinger · 1968
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A lower bound for the smallest eigenvalue of the Laplacian
J. Cheeger · 1970
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Lower bounds for the partitioning of graphs
W.E. Donath and A.J. Hoffman · 1973
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Algebraic connectivity of graphs
M. Fiedler · 1973
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A property of eigenvectors of nonnegative matrices and its applications to graph theory
M. Fiedler · 1975
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Isoperimetric constants and the first eigenvalue of a compact Riemannian manifold
S.-T. Yau · 1975
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Generalized extremal length of an infinite network
T. Nakamura and M. Yamasaki · 1976
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A relation between growth and the spectrum of the Laplacian
R. Brooks · 1981
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Difference equations, isoperimetric inequality and transience of certain random walks
J. Dodziuk · 1984
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λ 1 , \lambda_{1}, isoperimetric inequalities for graphs, and superconcentrators
N. Alon and V. D. Milman · 1985
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Spectral and function theory for combinatorial Laplacians
J. Dodziuk and L. Karp · 1988
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Isoperimetric inequalities, growth, and the spectrum of graphs
B. Mohar · 1988
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On the first eigenvalue of the combinatorial Laplacian for a graph
Y. Ohno and H. Urakawa · 1994
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Analysis on local Dirichlet spaces. I. Recurrence, conservativeness and L p L^{p} -Liouville properties
K.-T. Sturm · 1994
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Growth and the spectrum of the Laplacian of an infinite graph
K. Fujiwara · 1996
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Spectral Graph Theory
F.R.K. Chung · 1997
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p p -harmonic functions on graphs and manifolds
I. Holopainen and P.M. Soardi · 1997
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Complete manifolds with positive spectrum
P. Li and J. Wang · 2001
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On spectral clustering – analysis and an algorithm
A.Y. Ng, M.I. Jordan, and Y. Weiss · 2001
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Discrete Calculus: Applied Analysis on Graphs for Computational Science
L.J. Grady and J.R. Polimeni · 2010
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An inverse power method for nonlinear eigenproblems with applications in 1-spectral clustering and sparse PCA
M. Hein and T. Bühler · 2010
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Unbounded Laplacians on graphs: basic spectral properties and the heat equation
M. Keller and D. Lenz · 2010
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Gaussian upper bounds for heat kernels of continuous time simple random walks
M. Folz · 2011
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On stochastic completeness of jump processes
A. Grigor’yan, X. Huang, and J. Masamune · 2012
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Spectral Clustering and Biclustering
M. Bolla · 2013
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S. Amghibech · 2003
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Isoperimetric estimates for the first eigenvalue of the p-Laplace operator and the Cheeger constant
B. Kawohl and V. Fridman · 2003
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The spectrum of the p p -Laplacian and p p -harmonic morphisms on graphs
H. Takeuchi · 2003
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Semigroups and evolution equations: Functional calculus, regularity and kernel estimates
E. DiBenedetto, J.M. Urbano, and V. Vespri · 2004
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On the expansion of graphs of 0/1-polytopes
V. Kaibel · 2004
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A tutorial on spectral clustering
U. von Luxburg · 2007
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A note on self-adjoint extensions of the Laplacian on weighted graphs
X. Huang, M. Keller, J. Masamune, and R.K. Wojciechowski · 2013
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Volume growth and bounds for the essential spectrum for Dirichlet forms
S. Haeseler, M. Keller, and R.K. Wojciechowski · 2013
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Parabolic theory of the discrete p p -Laplace operator
D. Mugnolo · 2013
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Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory
L. Frank, D. Lenz, and D. Wingert · 2014
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Cheeger inequalities for unbounded graph Laplacians
F. Bauer, M. Keller, and R. Wojciechowski · 2015
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Time regularity and long-time behavior of parabolic p p -Laplace equations on infinite graphs
B. Hua and D. Mugnolo · 2015
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Intrinsic metrics on graphs – a survey
M. Keller · 2015
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