In this chapter, a review of some aspects of graph theory that are important for probabilistic graphical models are presented. After providing a definition of directed and undirected graphs, some basic theoretical graph concepts are introduced, including types of graphs, trajectories and circuits, and graph isomorphism. A section is dedicated to trees, an important type of graph. Some more advanced theoretical graph aspects required for inference in probabilistic models are introduced, including cliques, triangulated graphs, and perfect orderings. The chapter concludes with a description of the maximum cardinality search and graph filling algorithms.
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