The earliest work recognizable as network science came from the branch of mathematics known as graph theory. Graph theory originated with Leonhard Euler's 1736 solution (Euler, 1953) to the seven bridges problem. At the time, the city of Königsberg, Prussia (now Kaliningrad, Russia) had seven bridges connecting the banks of the Pregel River to two islands (pictured as follows). It was not known whether it was possible to find a path through the city that crossed every bridge exactly once. Euler showed that it was impossible, and he did so using new methods that became the basis for graph theory, and later for network science.
Leonhard Euler was a prolific 18th century mathematician. His surname is pronounced "oiler" (and his work does indeed lubricate the gears of modern mathematics). He is perhaps best remembered by his namesake: Euler's number, e ≈ 2.7 (which, confusingly, was discovered by Jacob Bernoulli):
Seventeenth-century Königsberg and its seven bridges
The study of networks also has a rich history in sociology. The sociologists, Jacob L. Moreno and Helen Hall Jennings proposed tools for the quantitative study of interpersonal relationships, which they called sociometry (Moreno & Jennings, 1934). These tools included the sociogram, a graphical representation of social networks very similar to the type of network diagrams currently in use.
When Moreno was hired by Fannie French Morse, superintendent of the New York Training School for Girls, to investigate a wave of runaways, it was sociograms that allowed him to visualize and communicate the nature of the social forces driving the runaways. Many of the tools used in modern network science—centrality, affiliation networks, community detection, and others—come from sociology. Over the past several decades, sociometry has branched into social network analysis, a rich and active subfield within network science.
Sociology is the science concerned with how individuals and their interactions produce institutions and societies. Networks are used in sociology to represent and quantify the relationships between individuals.
Various other fields have found it useful to study network structure, and have shared their tools and findings with each other as part of the interdisciplinary complex systems community. Ecologists study food webs—relationships between predator and prey species. Biologists study networks of interactions between genes. Physicists study magnetic interactions between neighboring atoms in crystals. All of these fields are doing exciting work with network science.
Complex systems are those that arise from the interactions of simpler components, for example, traffic from cars, stock markets from stock trades, and ecologies from species. Networks are used to analyze and study the interrelationships between components.
And then, of course, there's the internet. The internet itself is literally a network—computers and routers connected to each other by copper wire, fiber optic cables, and so on. But, on top of that, the content on the internet is also networked. Links between web pages form networks, and online social networks allow people to interact by friending or following each other. The Google search engine was founded on the PageRank algorithm (Page et al., 1999), a network-science-based approach to identifying popular websites. Online social networks typically make money by selling advertising space, and using network science to show ads to the people most likely to click on them. If you see a picture of a cute cat online, you can use network science to understand how the picture got to your computer screen, how the picture connects you with your friends, and what the picture tells you about other sites you might like to visit.
Online activity leaves digital trace data—records of activity stored in logs and databases. Digital trace data can often be used to construct networks of relationships between individuals. From these networks, it is surprisingly easy to predict many things, such as purchasing preferences (Zhang & Pennacchiotti, 2013), political ideology (Cohen & Ruths, 2013), and even sexual orientation (Jernigan & Mistree, 2009). The powerful techniques available for such data raises both exciting possibilities and complex ethical considerations.
