%0 Journal Article
%1 chayes2013mathematics
%A Chayes, Jennifer
%D 2013
%J Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
%K dynamics incentive math structure webscience
%N 1987
%T Mathematics of Web science: structure, dynamics and incentives
%U http://rsta.royalsocietypublishing.org/content/371/1987/20120377.abstract
%V 371
%X Dr Chayes’ talk described how, to a discrete mathematician, ‘all the world’s a graph, and all the people and domains merely vertices’. A graph is represented as a set of vertices V and a set of edges E, so that, for instance, in the World Wide Web, V is the set of pages and E the directed hyperlinks; in a social network, V is the people and E the set of relationships; and in the autonomous system Internet, V is the set of autonomous systems (such as AOL, Yahoo! and MSN) and E the set of connections. This means that mathematics can be used to study the Web (and other large graphs in the online world) in the following way: first, we can model online networks as large finite graphs; second, we can sample pieces of these graphs; third, we can understand and then control processes on these graphs; and fourth, we can develop algorithms for these graphs and apply them to improve the online experience.