Graph Theory is a branch of discrete mathematics sadly neglected in many curricula: it’s rare to find it in a high school syllabus and at some universities you can avoid it entirely and still get a major in mathematics: thus many students miss a chance to see exciting applications in computer science, business, psychology or sociology. However it is Topic 3 of Unit 3 in General Mathematics in our new National Curriculum.
Social network analysis relies on graphs to describe a wide variety of situations: the nodes might represent people, organizations, or places and the edges joining nodes can show friendship, financial interaction, sexual encounters, academic collaboration, costarring in movies (with or without Kevin Bacon) or just about any interaction you can imagine. Social network analysis has been used on everything from marketing and advertising, predicting epidemics, collapse in financial networks to tracing criminal networks. (Once upon a time it was very easy to create a graph of your friend network on Facebook but it’s a bit harder now.)
One type of graph called Sociograms were first developed by Jacob Moreno back in the early 1930’s and his work was reported in the New York Times as one of the first examples of using mathematical visualisation to study human relationships. He was mostly interested in interactions between school children. The Wikipedia page on sociograms has examples of primary school friendship networks that reveals some familiar patterns as kids get older (see if any of them remind you of your own experience). It’s also a topic in NSW in Stage 6 of Community and Family Studies. (A wonderful opportunity for maths teachers to work across disciplines). There use is only limited by imagination. Someone has even used them to map the inter-relationships between characters in various Shakespearean plays.
from Network visualization: mapping Shakespeare’s tragedies by Martin Grandjean
… to be continued …