where G is the graph considered, whereas the quantities I k ν, k μ are the so-called "exchange energies" between nearest-neighbours, which (in the energy units considered) assume the values ±1 (mathematically, this is a signed graph), while the S k ν · S k μ are inner products of scalar or vectorial spins or pseudo-spins. If the graph G has quadratic or triangular faces P, the so-called "plaquette variables" P W, "loop-products" of the following kind, appear: