Difference equations on weighted graphs

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Notes on averaging over acyclic digraphs and discrete coverage control (2006, methodology): “The work [11] analyzes the averaging algorithms in the framework of partial difference equations over graphs [15].”
Average consensus problems in networks of agents with delayed communications (2005, methodology): “The network of agents is modeled in the framework of Partial difference Equations (PdEs) introduced in [10] and used in [6] analyzing the property of various linear and nonlinear consensus protocols.”
Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing (2008, methodology): “Analogous definitions and properties have also been used in the context of semi-supervised learning [34] and differential calculus on graphs [37], [38].”
Distributed Coordination Control of Multiagent Systems While Preserving Connectedness (2007, background): “The graph Laplacian can be thought of as an encoding of the discrete topology heat equation [30]–[32], where differential operators can be defined for functions over graphs.”