Derivative Graphs in Global Structures of Bayesian Algebraic Networks

Abstract

The article is aimed at summarizing the concepts of a derivative graph and a primitive graph for graphs with backbone connectivity. Theorems are formulated and proved on the main connectedness of the graph of the derivative and on the primitive graph of the main connected graphs. The theoretical and practical significance of the result is to simplify the search for successful visualization of algebraic Bayesian networks, which would help to identify the features of their structure, as well as the definition of new types of global structures of these networks. Such structures would allow us to store the same information, but use other output algorithms, which would simplify the software implementation of this model. Note that maintaining the property of trunk connectivity when finding the graph of the derivative is considered in this article for the first time.