Analysis of the nonstar graphs of the Legendre transform in the ising model

Investigation (started in [1]) of the first Legendre transformation for the logarithm of the statistical sum in the Ising model is continued. The diagram expansion of the Legendre transformation $\Phi$ is the analogue of the virial expansion in the nonideal gas theory, however in contrast to the gas theory, in the case of the Ising model the functional $\Phi$ contains nonstar graphs as well. Complete characterisation of these graphs is given. The practical method of constructing the nonstar graphs (the compensation method) is suggested.