Many real-world phenomena can be phrased in terms of networks. For example, when studying the traffic congestion within a country, the road network describes the possible routes that cars and truck might take, and it provides the limits on the amount of traffic that can be managed. An electricity network describes how electricity can flow. The network of friendships between people describe who could communicate with whom so as to spread news or rumors. Many parts of the critical infrastructure of our society can be described in terms of networks, and as such networks form an important topic of research. On the NetworkPages, many examples of such research can be found.

A network consists of objects with connections between them, and possibly also properties of the objects and their connections. In a road network, the objects may be the cities, while the connections are given by the roads between them. The properties of the objects could correspond to the number of cars in the cities, while the properties of the connections could correspond to the lengths of the roads, the number of lanes they consist of, the amount of traffic, etc. The objects and the connections between them are modeled as graphs, see the explanation below. For computer networks, the computers are the objects, and they are connected to one another by physical cables. Properties of the connections could be the bandwidth of the cables, the amount of information sent along them, or even the delays of packets sent on the cables.

Societal needs often require that networks are controlled and engineered so as to function as efficiently as possible. In networks, often algorithms are used for this, see the explanation. Unpredictability and variability, for example in the amount of traffic in a road network, are common features of many networks, and dealing with uncertainty by robust methods is crucial to solve many societal problems. Hence, besides the theory of algorithms also probability theory plays an important role in the study of networks.