## 2.2 Networks and graphs (Ch. 2.2)

The components in a network are called **nodes** or **vertices** and the direct connections between them are called **links** or **edges**. When we are describing a network in real life, it’s better to use **networks**, **nodes**, and **links**, whereas **graphs**, **vertices**, and **edges** are mostly used for an abstract representation of networks. Some people do not care about these distinctions, though.

** N**, meaning the

**number of nodes**, is also called the

**size of the network**. Nodes are labeled as

**= 1,2,3,…,**

*i**N*

** L**, representing the

**total number of links**in a network.

For an individual link, we may represent it as \((i, j)\). For example, (2,4) denotes the link connecting nodes 2 and 4.

Links can either be **directed** or **undirected**. If I make a phone call to you, then the link between us is from me to you. It is **directed**. If we are friends on social media, then this link is **undirected**.

A network is **directed** if all of its links are **directed**. If all of its links are **undirected**, then this network is an **undirected** network.