11 October 2012
The use of formal mathematical models in sociology started in the 1940s and attracted mathematicians such as Frank Harary in the 1950s. The idea is to take the rather intuitive ideas described in social theory and express these in formal mathematical terms. Social network analysis is probably the best known of these and it is the area which has caught the imagination of a wider audience and has been the subject of a number of popular books. We shall give a brief over view of the field of social networks and will then look at three examples which have thrown up problems of interest to the mathematical community. We first look at positional analysis techniques and give a formulation that tries to capture the notion of social role by using graph coloration. We look at algebraic structures, properties, characterizations, algorithms and applications including food webs. Our second and related example looks at core-periphery structures in social networks. Our final example relates to what the network community refer to as two-mode data and a general approach to analyzing networks of this form. In all cases we shall look at the mathematics involved and discuss some open problems and areas of research that could benefit from new approaches and insights.
- Industrial and Applied Mathematics Seminar