Network Theory Overview

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In this module we will give an overview to the different questions that we are interested in trying to answer when it comes to analysing networks, this module also works as an overview to the content we will be covering during the rest of the course.​



Transcription:
In this section we are 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 will be covering. As the name implies network theory is all about the study of networks, we are trying to create models so as to analyze 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 standardized 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 analyze the question then turns to what are the features and properties of this network that we should be really interested. 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 our network we are interested in because as with all models we will be focusing on some information and excluding other.
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 we will 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 will be asking about our 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 effect the elements on the local level.
Here some of the key questions we will be asking about the overall structure to the network is firstly how connected is it? Are there connections between all the parts or are some parts disconnect 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 patters 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 we are interested in answering here is if we change some parameter to one of