Mathematics of Large Technological Evolving Networks

Sponsored by the UK's Engineering and Physical Sciences Research Council.
Grants: EPSRC , EP/I016058/1, EP/I016031/1 & EP/I017321/1
Project dates: January 2011 - January 2013


Connections are important. In studying nature, technology, commerce and the social sciences it often makes sense to focus on the pattern of interactions between individual components as networks. In addition, improvements in computing power have made it possible to gather, store and analyze large data sets, especially in the areas of fast moving consumer goods (who bought what), telecommunications (who phoned who), mobile devices (who travelled where) , on-line social networks (who Twittered to who) and energy (who switched on when).

This project aims to further advance this important area by addressing an important feature that has fo far received very little attention from the mathematical community: technological networks vary over time.  Indeed, such networks are common place:

  • in energy: fluctuations in power consumption by users across different times of the day and seasons,
  • in telecommunications: the time order of phone calls and text messages by users across time,
  • in transport: the time table of train stations, airports or ports connecting cities,
  • in the World Wide Web: the evolution of hyperlinks added and deleted between pages,
  • in online social networks: as friends are added and deleted,
  • in retail trade: networks of consumer similarity based on the seasonality of product demand.

Further, dynamic networks have important consequences, for example, if A phones B today and B phones C tomorrow, then a message may pass from A to C, but not from C to A. So there is an immediate lack of symmetry that makes much of the existing theory obsolete. Moreover, the patterns of connectivity that we see today may be different tomorrow. So there is built-in uncertainty about the future. In this proposal we will develop new mathematical techniques to study the type of dynamically evolving networks that are relevant in the Digital Economy, allowing researchers to discover the important players, quantify the efficiency of a network and predict future behaviour. These ideas offer immediate benefits outside academia, allowing us to tackle questions such as: who are the important broadcasters or receivers of information? who should we target our advertising campaign at? what will the network look like next week or next year? is there any suspicious activity today? which networks users appear to be underage? which customers are likely to change brand loyalty? how quickly will a rumour or virus spread? what would be the effect of changing the way that customers are charged for network usage?

Our objectives are to develop to practical, quantitative solutions to these issues by developing a new, underpinning mathematical framework that leads directly to useful computer software. In order to make sure that the results will have immediate benefit, we have put together a team of non-academic experts who use large technological networks in their businesses. These people will provide realistic data sets, pose specific challenges and provide regular feedback and advice throughout the project.

Academic Partners

University of Strathclyde
Dept. of Mathematics and Statistics, University of Strathclyde

Dept. of Mathematics and Statistics, University of Reading

Computer Laboratory, University of Cambridge

Industrial Partners

i2, Cambridge

DMarket Sentinel, London


14 January 2011

Kick-off meeting

The MOLTEN kick-off meeting will take place in Reading on the 17th of February 2011.

16 January 2011

MOLTEN Web-site is launched

The public MOLTEN web-site is now available.