Defining a network

Networks

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June 5^th 2018

The scientific study of networks is an interdisciplinary field that combines ideas from mathematics, physics, biology, computer science, statistics, the social sciences, and many other areas. It is a relatively understudied area of science, but its multidisciplinary nature means that an increasing amount of scientists are engaging with it.

A network is, in its simplest form, a collection of points joined together in pairs by lines. A point is referred to as a node or vertex and a line is referred to as an edge. Many systems of interest in the physical, biological, and social sciences can be thought of as networks, and there are four principle types of network:

1. Technological networks are the physical infrastructure networks that form the backbone of modern technological societies. Perhaps the most celebrated such network—and a relatively recent entry in the field—is the Internet, the global network of data connections that links computers and other information systems together.
2. Networks of information are networks consisting of items of data linked together in some way. Information networks are all, so far as we know, man-made, with perhaps the best known example being the World Wide Web, though many others exist and are worthy of study, particularly citation networks of various kinds.
3. In the scientific study of networks, the phrase “social networks” has a much broader meaning: a social network is any network in which the nodes represent people and the edges represent some form of connection between them, such as friendship.
4. Networks appear in many branches of biology as a convenient way of representing patterns of interaction between biological elements. Biological networks include metabolic networks, neural networks, and food webs.

These networks are simplified representations that reduce systems to an abstract structure or topology, capturing only the basics of connection patterns and little else. This makes the abstract study of its content and structure much clearer. The study of network structures is crucial, as understanding something about the structure of networks is essential to understanding fully how the corresponding systems work. Networks capture the pattern of interactions between the parts of a system, and these can have a large effect on the behaviour of a system.

See below for examples of each of the four types of network: from natural gas pipelines to 15th century Italian marriage ties.

Structure of the Internet: Technological Network

The Internet is the worldwide network of physical data connections between computers, phones, tablets, and other devices. The nodes and edges of the Internet fall into a number of different classes: the backbone of high-bandwidth long-distance connections; the ISPs, who connect to the backbone; and the end users home users, companies, and so forth – who connect to the ISPs.

Image credit: A schematic depiction of the structure of the Internet by Mark Newman. Used with permission.
Telephone network: Technological Network

The telephone network—meaning the network of landlines and wireless links that transmits telephone calls—is one of the oldest electronic communication networks still in use, but it has been studied relatively little by network scientists, primarily because of a lack of good data about its structure.

Image credit: A sketch of the three-tiered structure of a traditional telephone network by Mark Newman. Used with permission.
Natural gas pipelines in Europe: Technological Network

Above is an example of a distribution network. Distribution networks include things like oil and gas pipelines, water and sewerage lines, and the routes used by the post office and package delivery companies. The thickness of lines indicates the sizes of the pipes.

Image credit: Network of natural gas pipelines in Europe by R. Carvalho, L. Buzna, F. Bono, E. Gutierrez, W. Just, and D. Arrowsmith. Reprinted with permission. “Robustness of trans-European gas networks”, Phys. Rev. E 80, 016106 (2009). Copyright 2009 by the American Physical Society.
Pages on a corporate website: Information Network

The nodes in the above network represent pages on a website and the directed edges between them represent hyperlinks.

Image credit: A network of pages on a corporate website by Mark Newman. Used with permission.
A web crawler: Information Network

Web crawlers can be used to investigate the structure of the internet by automatically surfing the Web looking for pages. The network structure of the Web does not allow for all pages to be discovered, however.

Image credit: The operation of a web crawler by Mark Newman. Used with permission.
An ego-centered network: Social Network

This is the network surrounding one particular individual, meaning that individual plus his or her immediate contacts. The individual in question is referred to as the ego and the contacts as alters.

Image credit: An ego-centered network by Mark Newman. Used with permission.
Intermarriage network: Social Network

In this network, the nodes represent families and the edges represent ties of marriage between them.

Image credit: Intermarriage network of the ruling families of Florence in the fifteenth century by J.F. Padgett and C.K. Ansell. Reprinted with permission. “Robust Action and the Rise of the Medici, 1400-1434”, The American Journal of Sociology 98.6 (1993).
Protein folding: Biological Network

Proteins, which are long-chain polymers of amino acids, do not naturally remain in an open state, but collapse upon themselves to form a more compact folded state. Proteins that detect whether new genetic proteins need to be created form a genetic regulatory network. The nodes in this network are proteins or the genes that code for them, and a directed edge from gene A to gene B indicates that A regulates the expression of B.

Image credit: Protein folding. Copyright OUP 2018.
The structure of a neuron: Biological Network

At the simplest level, a neuron can be thought of as a unit that accepts a number of inputs, combines them, and generates an output that is sent to one or more further neurons. In network terms, a neural network can thus be represented as a set of nodes—the neurons—connected by two types of directed edges, one for excitatory inputs and one for inhibiting inputs.

Image credit: The structure of a neuron. Copyright OUP 2018.
A food web of species in Antarctica: Biological Network

Nodes in a food web represent species or sometimes, as with some of the nodes in this diagram, groups of related species, such as fish or birds. Directed edges represent predator–prey interactions and run in the direction of energy flow, i.e., from prey to predator.

Image credit: A food web of species in Antarctica by Mark Newman. Used with permission.