Network science

Network science studies systems as sets of nodes and connections, examining how their structure shapes processes such as communication, contagion, and coordination.

Graph theory: The mathematical study of graphs, consisting of vertices and edges. Provides the formal language for representing network structures.
Small-world network: A network with short average path lengths and substantial local clustering. It explains how networks can combine tight neighborhoods with rapid long-range reach.
Social network analysis: The study of social relationships using network representations and methods. It applies network measures to relationships, groups, and influence among people.
Leonhard Euler: An eighteenth-century mathematician whose work on the Königsberg bridges problem helped establish graph theory. His abstraction of places and bridges supplied an early mathematical foundation for network study.
Six degrees of separation: The idea that any two people can be connected through a short chain of social acquaintances. It expresses how sparse links can make vast social networks surprisingly navigable.
Degree (graph theory): The number of edges incident to a vertex in a graph. Degree measures how many direct connections each network node has.
Scale-free network: A network whose degree distribution has a heavy tail, often approximated by a power law. Its hubs make connectivity and vulnerability differ sharply from random-network expectations.
Biological network: A network representing interactions among biological entities such as genes, proteins, or organisms. Biological systems use interconnected components whose organization affects function.
Paul Erdős: A Hungarian mathematician known for major contributions to graph theory and probabilistic methods. His work helped make random graphs a central model of network structure.
Robustness (network science): A network’s ability to retain connectivity or function under failures and disruptions. It provides a framework for assessing whether network structure protects or endangers a system.

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