Network science

Network science is the study of how complex systems can be understood by looking at them as networks made up of nodes and links. Nodes are the parts of the system, such as people, computers, or proteins, while links are the connections between them, such as friendships, internet cables, or chemical reactions. By studying these connections, scientists can understand why information spreads quickly in some places, how diseases move through populations, or why failures in part of a power grid can lead to blackouts.^[1] Networks can be found in both nature and human-made systems, including social media, ecosystems, and the World Wide Web. Interestingly, many networks share similar patterns, like groups of nodes clustering together, short paths that connect almost everyone, or a few very important nodes with many more links than others.^[2]

Internet network map

The roots of network science come from graph theory in mathematics. In the 18th century, mathematician Leonhard Euler solved the famous Seven Bridges of Königsberg problem, introducing the idea of nodes and edges to represent connections.^[3] Later, in the 20th century, Paul Erdős and Alfréd Rényi studied random graphs, which showed how probability affects whether connections form in large networks.^[4] In the 1990s, Albert-László Barabási and Réka Albert discovered scale-free networks, where a few highly connected nodes, called hubs, hold much of the system together.^[5] Examples include airline routes, where a few major airports connect most flights, or the internet backbone, where certain servers handle massive amounts of traffic. This finding revealed that many real networks are not completely random, but follow patterns that make them stable against random failures yet vulnerable if their hubs are attacked.^[6]

Because networks appear in so many places, network science is an interdisciplinary field that connects physics, biology, sociology, computer science, and economics.^[7] In medicine, networks are used to model how diseases like COVID-19 spread, helping predict outbreaks and test strategies such as vaccinations.^[8] In neuroscience, brain networks help explain how neurons communicate and how disruptions may cause conditions like epilepsy or Alzheimer's disease.^[9] In technology, network science improves search engines, cybersecurity, and transportation systems by studying efficiency and weak points. Financial systems can also be studied as networks, where banks and institutions are linked, showing how one failure can spread risk across the whole system.^[10]

A major goal of network science is to find universal patterns that apply to many different networks. One example is the power-law distribution, where most nodes have only a few connections but a few nodes have many, like celebrities on social media compared to average users.^[11] Another example is the small-world property, which shows that most nodes can be reached by only a few steps. This was famously demonstrated in Stanley Milgram’s “six degrees of separation” experiment, which suggested that any two people are connected by only a few acquaintances.^[12] Scientists also study motifs, which are small recurring patterns, such as feedback loops in genetic networks, that act as building blocks for larger systems.^[13]

Today, network science is expanding rapidly thanks to the growth of big data. Researchers now study networks with millions of nodes and billions of links, such as genetic networks, online platforms, and global communication systems.^[14] New areas of study include dynamic networks, which change over time as relationships form or break, and multilayer networks, where nodes are connected in several ways at once, such as people interacting online and face-to-face.^[15] By analyzing these systems, network science helps explain how complexity can arise from simple connections, and it provides tools to solve problems ranging from protecting ecosystems to understanding how fake news spreads online.^[16]