  We introduce a concept of isoperimetric dimension for magnetic graphs, that
is, graphs where every edge is assigned a complex number of modulus one. In
analogy with the classical case, we show that isoperimetric inequalities imply
Sobolev inequalities on such graphs. As a first application, we show that the
signed Cheeger constant behaves additively with respect to Cartesian products
of graphs. Using heat kernel techniques, we also give lower bounds for the
eigenvalues of the discrete magnetic Laplacian.
