An isoperimetric constant for signed graphs

A sign in the usual Laplacian on graphs is introduced 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.