An isoperimetric constant for signed graphs

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.