Algebraic bayesian network maximal join graph cliques structual analysis

The secondary structure, usually represented in a form of a join graph, is very sufficient in algebraic Bayesian networks (ABN) presentation and processing and minimal join graphs are the most effective variation of such a structure for ABN main algorithms probabilistic logic inference work. The goal of this work is the designing of exhaustive classification for special minimal join graph subgraphs called possessions. A system of term is given to structure the research space. A classification of possessions is compiled and researched. The classification is proven to be exhaustive. The classification is proven to be a consistent extension for the one used before. The obtained results are the basement for the further ABN global structure researches, in particular, in such the questions as the questions of minimal join graph set cardinal number, clique classification, their inner structure researches and minimal join graph set synthesis algorithms improvements.