The paper considers algorithms for global structures generation in algebraic Bayesian networks. A decremental algorithm for constructing a secondary structure after deleting vertex from the adjacency graph is proposed supplemented by a listing of the algorithm code and by the proof of its correctness. The results of the statistical tests for decremental algorithm are proposed graphically together with a comparative analysis of the results. Moreover, the description of incremental algorithm for adding vertex in tertiary structure is provided supplemented by a listing of the algorithm code and proof of its correctness.