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A graphical model consists of I a graph G = (V,E) and a V set of properties that determine a family of V probability distributions. There are many different types of graphs and properties, each determining a family. It is common to be able to develop algorithms that work for all members of the family by considering only a graph and its properties. Thus, solving difficult problems (such as deriving an approximation to an NP-complete optimization problem) might become worthwhile only because a solution can be applied many times for different problem instances.