Network science is the area of science and mathematics that tries to analyze and interpret networks based upon data and the use of computer software. Network science is supported by the formal language of graph theory, a relatively new area of mathematics that provides a standardized language with which to talk about and quantify the structure and properties of networks. Presented with a network to analyze, the question turns to what are the features and properties of this network that are of real interest?
The first set of questions we might like to ask relate to individual elements within the network. We want to know what are the nodes within the network, what are the connections between them, and what properties are we really interested in. For example, in a computer network we might not be interested in who owns the different computers and connections, but just interested in the speed of the computers and the bandwidth of the connections. So we need to define what it is about the network we are interested in because as with all models we will be focusing on some information and excluding another. There is lots of other information we want to know about these individual elements and the connections, such as asking whether they are weighted or not, meaning can we ascribe a value to them. We can talk about a computer network’s bandwidth in megabits per second, but it might not be so easy to do the same with a social network where the relations are of friendship or kinship. We can also ask if these relations go both ways or are just unidirectional. Other questions one might be interested in asking here is how connected is any individual node or how central is it within the overall network.
The next major set of questions one might ask about a network will relate to its overall structure. Networks are defined by both what happens on the local level, that is how central or connected you are, but also what happens on the global level because the dynamics of the network on the global level feeds back to affect the elements on the local level. Here some of the key questions one might ask about the overall structure of the network include; Firstly, how connected is it? Are there connections between all the parts or are some parts disconnected and separate from others? How dense is this set of connections? If we compare a group of unassociated people waiting at a bus stop with a close-knit group of friends, we will see the density of the network will vary greatly. What are the patterns of clustering within the system? Do we see many small groups or just a few large groups? These are the types of features that will define the overall makeup of the network structure. One key question one might be interested in answering here is if we change some parameter to one of these properties, that is, increase or decrease its value, how will that affect the overall structure to the system?
Types of Networks
The possible ways in which we can connect even a few elements grows very quickly, and there is of course many different structures to networks possible. It is not possible to create a list of all of these, but what we can do is try and identify some fundamentally different types or models to networks. The first type of network that researchers started to explore was what is called a random network. By studying randomly generated networks, we get an important insight, which is that most networks are not random. They are created and often defined by the rules under which the elements chose to connect to other elements within the network. Sometimes networks are specifically designed in a top-down fashion, such as the computer network within a corporation, where some systems administrator has specifically designed it in a particular way. But many of the networks we see around us are not like this. Within many networks such as commercial market, logistics networks, friendship networks, terrorist networks, food webs and so on, the overall network emerges out of local level rules and interactions. When one begins to understand these rules, then one can begin to understand the different types of overall network structures that emerge out of them.
The next set of questions one might want to ask about a network relates to how something will spread out or travel along the network, and this is referred to as diffusion. If we are trying to understand the outbreak of a disease in a given area, we will be trying to understand how it is spreading and what network structures will give rise to rapid or delayed spreading. One would also be interested in how changing a given parameter would affect this. There will be times when diffusion is a positive thing and times when it is not, here we will be talking about how to contain it to prevent disaster spreading. And this would lead naturally to a discussion on network robustness and fragility, how susceptible is the network to failure both from random and strategic attack.
Lastly, how networks change over time presents another set of questions about the network we are analyzing. How does something like the network to a political regime come to form? What are the mechanisms that hold it together? And when does it disintegrate?