On uniqueness class for a heat equation on graphs

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Volume growth and stochastic completeness of graphs (2012, methodology): “However, the recent paper of Huang [20] shows that a certain uniqueness class for the heat equation (with close connections to stochastic completeness) is very diﬀerent for graphs and manifolds.”
On the conservativeness and the recurrence of symmetric jump-diffusions (2012, background): “Recently, there has been a tremendous amount of work devoted to the conservation property of a non-local Dirichelt form; for instance, the physical Laplacian on an infinite graph [7, 6, 39, 40, 41, 24, 18, 19, 20] and non-local Dirichlet forms [26, 15, 31]; however, as far as the authors know, there”
Cheeger inequalities for unbounded graph Laplacians (2012, background): “[14, 15, 16, 23, 25, 30, 31, 32, 42], where certain variations of the concept also go under the name of adapted metrics.”
A note on self-adjoint extensions of the Laplacian on weighted graphs (2012, methodology): “In the context of stochastic completeness for jump processes see the work of Masamune/ Uemura [38], Grigor’yan/Huang/Masamune [20] and also [25, 26].”