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We consider the nonlinear graph $p$-Laplacian and its set of eigenvalues and associated eigenfunctions of this operator defined by a variational principle.
A lower bound for the smallest eigenvalue of the Laplacian
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λ 1 \lambda_{1} , isoperimetric inequalities for graphs, and superconcentrators
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Eigenvalues and expanders, Theory of computing
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Bounds on the L 2 L^{2} spectrum for Markov chains and Markov processes: a generalization of Cheeger’s inequality
G. F. Lawler and A. D. Sokal · 1988
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Graph partitioning by eigenvectors
D. L. Powers · 1988
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Isoperimetric numbers of graphs
B. Mohar · 1989
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Approximate counting, uniform generation and rapidly mixing Markov chains
A. Sinclar and M. Jerrum · 1989
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Solvability and bifurcations of nonlinear equations
P. Dràbek · 1992
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Multiplicitére des valeurs propres Laplaciens discrete et Laplaciens continus
C. de Verdière · 1993
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Some remarkable sine and cosine functions
P. Lindqvist · 1995
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On the second eigenvalue of the p p -Laplacian
A. Anane and N. Tsouli · 1996
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Upper bounds for eigenvalues of the discrete and continuous Laplace operators
F Chung, A. Grigor’Yan, and S.-T. Yau · 1996
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Spectral Graph Theory
F Chung · 1997
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Perron-Frobenius type results and discrete versions of nodal domain theorems
A. M. Duval and V. Reiner · 1999
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Discrete nodal domain theorems
E. B. Davies, G. M. L. Gladwell, J. Leydold, and P. F. Stadler · 2001
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Spectral clustering based on the graph p p -Laplacian
T. Bühler and M. Hein · 2009
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Handbook of Applied Analysis
N. S. Papageorgiou and S. Th. Kyritsi-Yiallourou · 2009
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PageRank and Random Walks on Graphs
F. Chung and W. Zhao · 2010
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On the isoperimetric spectrum of graphs and its approximations
A. Daneshgar, H. Hajiabolhassan, and R. Javadi · 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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On nodal domains and higher-order Cheeger inequalities of finite reversible Markov processes
A. Daneshgar, R. Javadi, and L. Miclo · 2012
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P. Rehák · 2001
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Half-Linear Differential Equations
O. Doslý · 2002
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On the generalization of the Courant Nodal domain theorem
P. Dràbek · 2002
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Eigenvalues of the discrete p p -Laplacian for graphs
S. Amghibech · 2003
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Expander graphs and their applications
S Hoory, N Linial, and A Wigderson · 2006
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A lower bound for nodal count on discrete and metric graphs
G. Berkolaiko · 2008
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Multi-way spectral partitioning and higher-order Cheeger inequalities
J. R. Lee, S. Oveis Gharan, and L. Trevisan · 2012
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Nodal domain and eigenvalue multiplicity of graphs
H. Xu and S.-T. Yau · 2012
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Improved Cheeger’s inequality: Analysis of spectral partitioning algorithms through higher order spectral gap
T.-C. Kwok, L.-C. Lau, Y.-T. Lee, S. Oveis Gharan, and L. Trevisan · 2013
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Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems
M. Struwe · 2013
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An algebraic analysis of the graph modularity
D. Fasino and F. Tudisco · 2014
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The optimal partition problem for p p -Laplacian eigenvalues as p p goes to one
M. Caroccia · 2015
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General Cheeger inequalities for p p -Laplacians on graphs
M. Keller and D. Mungolo · 2015
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Spectrum of the 1-Laplacian and Cheeger’s constant on graphs
K. C. Chang · 2016
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