F. R. Chung and S. Sternberg, Laplacian and vibrational spectra for homogeneous graphs, Journal of Graph Theory, vol.347, issue.6, pp.605-627, 1992.
DOI : 10.1002/jgt.3190160607

C. Deverdì-ere, Y. Torki-hamza, N. Truc, and F. , Essential self-adjointness for combinatorial Schrödinger operators II-Metrically non complete graphs, Math. Phys. Anal. and Geom, vol.14, pp.21-38, 2011.

C. Deverdì-ere, Y. Torki-hamza, N. Truc, and F. , Essential self-adjointness for combinatorial Schrödinger operators II-Metrically non complete graphs

C. Deverdì-ere, Y. Torki-hamza, N. Truc, and F. , Essential self-adjointness for combinatorial Schrödinger operators III-Magnetic fields, Ann. Fac. Sci. Toulouse Math, vol.20, issue.6, pp.599-611, 2011.

C. Deverdì-ere and Y. , Truc, F: Confining quantum particles with a purely magnetic field, Ann. Inst. Fourier (Grenoble), vol.60, issue.7, pp.2333-2356, 2010.

J. Dodziuk and V. Mathai, Kato???s inequality and asymptotic spectral properties for discrete magnetic Laplacians, In: Contemporary Mathematics, vol.398, pp.69-81, 2006.
DOI : 10.1090/conm/398/07484
URL : http://arxiv.org/abs/math/0312450

K. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations. Graduate Texts in Mathematics 194, 2000.

M. Folz, Gaussian Upper Bounds for Heat Kernels of Continuous Time Simple Random Walks, Electronic Journal of Probability, vol.16, issue.0, pp.1693-1722, 2011.
DOI : 10.1214/EJP.v16-926

R. L. Frank, D. Lenz, and D. Wingert, Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory, Journal of Functional Analysis, vol.266, issue.8, pp.4765-4808, 2014.
DOI : 10.1016/j.jfa.2014.02.008

B. Güneysu, M. Keller, and M. Schmidt, A Feynman?Kac?Itô formula for magnetic Schrödinger operators on graphs

B. Güneysu, O. Milatovic, and F. Truc, Generalized Schrödinger semigroups on infinite graphs. Potential Anal, pp.517-541, 2014.

S. Haeseler and M. Keller, Generalized Solutions and Spectrum for Dirichlet Forms on Graphs, In: Random Walks, Boundaries and Spectra. Progress in Probability Birkhäuser, vol.64, pp.181-199, 2011.
DOI : 10.1007/978-3-0346-0244-0_10

B. Hua and M. Keller, Harmonic functions of general graph Laplacians, Calculus of Variations and Partial Differential Equations, vol.25, issue.7, pp.343-362, 2014.
DOI : 10.1007/s00526-013-0677-6

X. Huang, On stochastic completeness of weighted graphs, 2011.

X. Huang, M. Keller, J. Masamune, and R. K. Wojciechowski, A note on self-adjoint extensions of the Laplacian on weighted graphs, Journal of Functional Analysis, vol.265, issue.8, pp.1556-1578, 2013.
DOI : 10.1016/j.jfa.2013.06.004

T. Kato, Perturbation Theory for Linear Operators, 1980.

T. Kato, L p -theory of Schrödinger operators with a singular potential In: Aspects of Positivity in Functional Analysis, pp.63-78, 1986.

M. Keller and D. Lenz, Unbounded Laplacians on Graphs: Basic Spectral Properties and the Heat Equation, Mathematical Modelling of Natural Phenomena, vol.5, issue.4, pp.198-224, 2010.
DOI : 10.1051/mmnp/20105409

M. Keller and D. Lenz, Dirichlet forms and stochastic completneness of graphs and subgraphs, J. Reine Angew. Math, vol.666, pp.189-223, 2012.

R. Kenyon, Spanning forests and the vector bundle Laplacian, The Annals of Probability, vol.39, issue.5, pp.1983-2017, 2011.
DOI : 10.1214/10-AOP596

J. Masamune, A Liouville property and its application to the Laplacian of an infinite graph, In: Contemporary Mathematics, vol.484, pp.103-115, 2009.
DOI : 10.1090/conm/484/09468

J. Masamune and T. Uemura, Conservation property of symmetric jump processes, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.47, issue.3, pp.650-662, 2011.
DOI : 10.1214/09-AIHP368

O. Milatovic, On m-Accretivity of Perturbed Bochner Laplacian in L p Spaces on Riemannian Manifolds, Integral Equations and Operator Theory, vol.52, issue.2, pp.243-254, 2010.
DOI : 10.1007/s00020-010-1800-0

O. Milatovic, Essential Self-adjointness of Magnetic Schr??dinger Operators on Locally Finite Graphs, Integral Equations and Operator Theory, vol.58, issue.3, pp.13-27, 2011.
DOI : 10.1007/s00020-011-1882-3

O. Milatovic and F. Truc, Self-Adjoint Extensions of Discrete Magnetic Schr??dinger Operators, Annales Henri Poincar??, vol.2, issue.7, pp.917-936, 2014.
DOI : 10.1007/s00023-013-0261-9

M. Reed and B. Simon, Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness, 1975.

A. Singer and H. Wu, Vector diffusion maps and the connection Laplacian, Communications on Pure and Applied Mathematics, vol.26, issue.8, pp.1067-1144, 2012.
DOI : 10.1002/cpa.21395