A complex system has many constituent parts which interact with one another in various, usually complicated ways. Thus, modelling complex systems is problematic and usually involves some simplifications.

The Earth’s climate is an important example. Biological systems, whether in the case of a single cell or an individual organism or species’ interactions, are complex systems. Many aspects of human existence and society—use of the Internet, spread of disease, population movements, economies—are all complex systems.

Complex systems are commonly represented as networks with vertices representing the parts and edges representing interactions. As the number of individual elements may be too great to treat each as a part, homogeneous subsets may be compartmentalized together; for example, an entire city may be treated as a single component.