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We consider Lipschitz- and Arens-Eells-type function spaces constructed formagnetic graphs, which are adapted to this setting from the area of optimaltransport on discrete spaces. After establishing the duality between thesespaces, we prove a characterization of the extreme points of the unit ball inthe magnetic Lipschitz space as well as a result identifying the magneticArens-Eells space as a quotient of the classical Arens-Eells space of anassociated classical graph called the lift graph.

Kantorovich Duality and Optimal Transport Problems on Magnetic Graphs