Mathematical sociology is not an oxymoron

Professor Martin G Everett, University of Manchester

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Dec 14, 2017
from 05:00 PM to 06:00 PM


Bennett LT8

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Abstract: The use of formal mathematical models in sociology started in the1940s 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 or four xamples which have become 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 third example relates to what the network community refer to as two-mode data and a general approach to analyzing networks of this form. If we have time we shall look at network diffusion and a possible connection to Bass models. 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.

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