The Algebraic Bayesian Network Tertiary Structure

Algebraic Bayesian network (ABN) tertiary structure is required to both a random minimal join graph and the minimal join graph set. In addition, it is required to find the best or an optimal secondary structure over the given ABN primary structure. The goal of the work is to create a clear definition of the ABN tertiary structure and associated objects on the basis of analysis of existing approaches and study of their properties. All existing approaches to the definition of “clique”, “clique set” and “clique graph”, and classification of the maximal join graph cliques are overviewed. A unified vocabulary for describing the associated objects satisfying the criteria of non-redundancy and systematization completeness is suggested. Tertiary polystructure is defined as a family of graphs constructed on subsets of the maximum join graph narrowings set whose edges are matched to specific relationships defined in the article. Tertiary structure is defined as a directed graph whose edges lead from the parent vertices to their sons, and whose vertices are the maximum join graph narrowing on weights of the edges and the vertices, as well as on the empty weight (parent graph over extended set of useful cliques).