## What is a graph?

A graph is a collection of vertices and edges that connect the vertices. *Figure 1* gives a visual representation of an example of a graph. There are a few features to note here, which we will discuss next:

**Undirected graph**: An undirected graph is a graph in which the edges have no direction, as shown in*Figure 1*.**Directed graph**: This is a graph in which the edges have a direction.**Path**: A path is a sequence of edges that connects a set of vertices that are distinct from one another, except the first and the last vertices as they may be the same. For example, in*Figure 1*, the edges**AB**,**BD**, and**DE**represent a path. It can also be described as the**ABDE**path, which does not repeat its vertices. In the case of a directed graph, the edges must traverse only in the specified direction to form the sequence of edges required to make a path.**Cycle**: A cycle is a path with at least two vertices involved; it starts and ends on the same vertex. For...