Sibling criterion for cyclicity of minimal joint graphs

Due to the inability of some algorithms for global logical and probabilistic inference on cyclic secondary structure of algebraic Bayesian network (ABN) and a relatively large time complexity of the algorithm for constructing such a structure it’s appropriate to present a criterion which allows checking if the ABN is cycling before building the secondary structure. The paper offers such criterion, based on the analysis of the support structure (semi-sibling graph).