 In this section, we're going to give an overview to network theory that will also work as an overview to the structure of this course and the content we'll be covering. As the name implies, network theory is all about the study of networks. We're trying to create models so as to analyse them. In order to be able to do this, the first thing we need is some kind of formal language and this formal language is called graph theory. We will be going into the details of graph theory in the next lecture, but it is a relatively new area of mathematics that gives us some kind of standardised language with which to talk about and quantify the structure and properties of networks. So once we have this basic vocabulary, say you give me a network to analyse. The question then turns to what are the features and properties of this network that we should really be interested in. We want to know what are the nodes within the network and what properties about them 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 firstly define what it is about our network that we're really interested in, because as with all models, we'll be focusing on some information and excluding other. There is lots of other information that we want to know about these individual elements and the connections between them, such as asking whether they are weighted or not, meaning can we ascribe some 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, whether relations are a friendship or kinship. We can also ask whether these relations are going both ways or are just unidirectional. Other questions that we'll be asking here is how connected is any individual node or how central is it within the overall network. The next major set of questions we'll be asking about our network will relate to its overall structure. Because networks are defined by both what happens on the local level, that is how central or connected they are, but also what happens on the global level, because the nature and dynamics of the network on the global level feeds back to affect the elements on the local level. Here some of the primary questions we'll be asking about the overall structure to the network is firstly how connected is it. Are these 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 closely knit group of friends, we'll see the density of the network will vary greatly. What then 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. Another key question we're 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? And we'll be discussing all of this in a later module. The possible ways in which we can connect even a very few elements grows very quickly. And there is of course many, many different structures to networks out there. We can't possibly 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 the 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 aren't 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 a 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 in fact not like this. Within many networks such as commercial markets, logistics networks, friendship networks, terrorist networks, food webs within ecosystems and so on. The overall network emerges out of local level rules and interactions. When we begin to understand these rules, then we can begin to understand the different types of overall network structure that emerges out of them. The next set of questions that we might want to ask about a network relate to how something will spread out or travel across 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 structure will give rise to a rapid or delayed spreading. We will also be interested in how changing a given parameter will affect this. There will be times when diffusion is a positive thing and times when it is not. In such circumstances we will be talking about how to contain it to prevent disaster spreading and this will lead us naturally to a discussion on network robustness and fragility. How susceptible is our network to failure both from random and strategic attack? Lastly, how networks change over time will present us with another set of questions about the network we are analysing. Will something like the network to a political regime come to form? What are the mechanisms that hold it together and when does it disintegrate? We will be discussing this life cycle to networks in our last module on network dynamics. This set of broad questions that make up the four main sections to our course should cover most of what we want to know about networks.