  A sign is introduced in the usual Laplacian on graphs and the corresponding
analogue of the isoperimetric constant for this Laplacian is presented, i.e. a
geometric quantity which enables to bound from above and below the first
eigenvalue. The introduction of the sign in the Laplacian is motivated by the
study of $2$-lifts of graphs and of the combinatorial Laplacian in higher
degree.
