# Introducing graph properties

In graph theory, a graph is a mathematical structure consisting of a set of objects, called **vertices** or **nodes**, and a set of connections, called **edges**, which link pairs of vertices. The notation is used to represent a graph, where is the graph, is the set of vertices, and is the set of edges.

The nodes of a graph can represent any objects, such as cities, people, web pages, or molecules, and the edges represent the relationships or connections between them, such as physical roads, social relationships, hyperlinks, or chemical bonds.

This section provides an overview of fundamental graph properties that will be used extensively in later chapters.

## Directed graphs

One of the most basic properties of a graph is whether it is directed or undirected. In a **directed graph**, also called a **digraph**, each edge has a direction or orientation. This means that the edge connects two nodes in a particular direction, where one node is the source and the other...