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In the simplest case, the network structure of the model is a directed acyclic graph (DAG). Then the GM represents a factorization of the joint probability of all random variables. More precisely, if the events are

X₁, ..., X_n,

then the joint probability

P(X₁, ..., X_n),

is equal to the product of the conditional probabilities

P(X_i | parents of X_i) for i = 1,...,n.

In other words, the joint distribution factors into a product of conditional distributions. The graph structure indicates direct dependencies among random variables. Any two nodes that are not in a descendant/ancestor relationship are conditionally independent given the values of their parents.