## Graph concepts

Next, we will briefly revisit the concepts from graph theory and some of the definitions that we will use in this chapter.

### Graph structure and properties

A graph is defined as a data structure containing nodes and edges connecting these nodes. In the context of this chapter, the random variables are represented as nodes, and edges show connections between the random variables.

Formally, if *X = {X*_{1}*, X*_{2}*,….X*_{k}*}* where *X*_{1}*, X*_{2}*,….X*_{k} are random variables representing the nodes, then there can either be a directed edge belonging to the set e, for example, between the nodes given by or an **undirected edge** , and the graph is defined as a data structure . A graph is said to be a **directed graph** when every edge in the set e between nodes from set **X** is directed and similarly an **undirected graph** is one where every edge between the nodes is undirected as shown in *Figure 1*. Also, if there is a graph that has both directed and undirected edges, the notation of represents an edge that may be...