Here each vertex i of the graph is a spin site that takes a spin value σ σ i = ± ± 1 . A given spin configuration σ σ partitions the set of vertices V ( G ) into two σ σ -depended subsets, those with spin up V + and those with spin down V − − . We denote by δ δ ( V + ) the σ σ -depended set of edges that connects the two complementary vertex subsets V + and V − − . The size | δ δ ( V + ) | of the cut δ δ ( V + ) to bipartite the weighted undirected graph G can be defined as