Research questions and chosen disciplines no comments
Hello! Sorry for the tardiness of my first post.
My research questions are (currently):
How can we make an effective mathematical model of the web? How can we make an effective mathematical model of social networking sites? How can we best use these models to “understand” the web and how people use the web?
These questions are rather vague and hopefully they will be refined over the next four years.
In order to make such a mathematical model we must decide what basic properties the model should have. This argument appears circular, needing to know properties of the web in order to make a model which will inform us of properties of the web! However, we are really investigating the (sometimes hidden) effects of these known properties and what they mean for the web.
For example we might want to model Facebook. We could associate Facebook with a graph G by assigning people to nodes and then draw an arc between two people if they are friends. Since it has been shown that two people with mutual friends are more likely to be friends themselves than two people with no mutual friends, one property of G is that it has an abundance of triangles. This means that if node A is joined to node C and node B is joined to node C then it is likely that node A is joined to node B.
In practice drawing G would be virtually impossible because Facebook changes constantly as new friendships are created and destroyed and people join and leave Facebook we make a model graph M (a more convenient graph which we generate and can control). In order to be a good model M must have an abundance of triangles.
Note that the seemingly abstract mathematical property, an abundance of triangles, comes about for a sociological reason. What other properties should the model graph have? To find this out it will be vital to understand how people use the web, so I have chosen to study sociology/philosophy as my first discipline.
Such mathematical models could be used to find the most efficient route from node to node (in the Facebook example from one person to another and be useful at looking at the spreading of ideas). These models could also be used to measure the resilience of a network from attack, (i.e. how will a network cope if we knock out some nodes?) hence I have chosen criminology as my second discipline.