What is a Network?

In 1736, a Swiss mathematician pondered routes for a sightseeing trip along the Pregel River in K?nigsberg. In 1880, an Italian painter turned zoologist sought to settle a hotly-contested controversy: whether or not birds protect crops by reducing insect populations. In 1932, the superintendent of a girls' reformatory school in Hudson, New York, hired a sociologist to investigate the cause of a recent wave of runaways. In 1955, a U.S. Army General and a mathematician developed a technique for identifying bottlenecks in the Soviet railway system. And, in 1998, two mathematicians in Ithaca, New York tried to figure out (among other things) why exactly all movie stars seem to be connected by Kevin Bacon.

These puzzles, taking place at different times and different places, might, at first glance, appear unrelated. But they have one thing in common: they all revolve around relationships – between people, between places, or between species – and they were all solved using the science of relationships, which has come to be known as network science. Interest in network science has grown considerably in recent years, as online social network platforms, such as Facebook, Twitter, WeChat, and Mastodon, have become increasingly popular.

This book covers the fundamental concepts of network science, as well as how to put them into practice using the Python-based NetworkX package. Part I (Chapter 1, What is a Network?, to Chapter 4, Affiliation Networks) introduces the concept of a network, as well as how to build, manipulate, and visualize networks in NetworkX. Part II (Chapter 5, The Small Scale – Nodes and Centrality, to Chapter 7, In-Between – Communities) demonstrates how to analyze network structure at various scales. Part III (Chapter 8, Social Networks and Going Viral, to Chapter 11, Visualization) applies network science to understanding complex systems using modeling, simulation, and visualization. In this introductory chapter, you'll learn some of the history of network science and the differences between common types of networks. You'll also see examples of different ways that relationships in a network can be interpreted. Finally, you'll get to build and visualize your first network using NetworkX!

In this chapter, we will cover the following topics:

• Network science: Learn the history of the study of networks.
• What is a network?: Understand the fundamental concepts of network science.
• What is NetworkX?: Getting familiar with the NetworkX Python package.
• Types of networks: Meet common variants of networks, and understand their applications.
• Your first network in NetworkX: Try a simple example.