# Graphs and NetworksIntroduction

Every day we are surrounded by countless connections and networks: roads and rail tracks, phone lines, the internet, electronic circuits and even molecular bonds. There are even *social networks* between friends and families. Can you think of any other examples?

In mathematics, all these examples can be represented as **graphs***graph* of a function). A graph consists of certain *points* called

**Graph theory** is the study of graphs and their properties. It is one of the most exciting and visual areas of mathematics, and has countless important applications.

We can draw the layout of simple graphs using circles and lines. The position of the vertices and the length of the edges is irrelevant – we only care about *how they are connected* to each other. The edges can even cross each other, and don’t have to be straight.

We can create new graphs from an existing graph by removing some of the vertices and edges. The result is called a **subgraph**

We say that the **order****degree**

Order:

Order:

Degree:

Degree:

Graphs that consist of a single loop of vertices are called **cycles**

Equipped with these new definitions, let’s explore some of the fascinating properties and applications of graphs.