Frustration and isoperimetric inequalities for signed graphs
Let G z V E z be a connected signed graph. Using the equivalence between signed graphs and 2 lifts of graphs, we show that the frustration index of G z is bounded from below and above by expressions involving another graph invariant, the smallest eigenvalue of the (signed) Laplacian of G z From the proof, stricter bounds are derived. Additionally, we show that the frustration index is the solution to a l 1 norm optimization problem over the 2 lift of the signed graph. This leads to a practical implementation to compute the frustration index. Also, leveraging the 2 lifts representation of signed graphs, a straightforward proof of Harary's theorem on balanced graphs is derived. Finally, real world examples are considered.
Discret. Appl. Math.