Exploring networks: the contribution historical evidence for social networks can make to the modern use of network theory

The mathematical understanding of networks has increased dramatically over the past ten years and network theory is being increasingly applied to practical problems in business and society. However, the gathering of evidence is often difficult. Experts in the field with formal qualifications in economics, maths, statistics and physics are accustomed to working with quantitative data, however the best information specific to the problem is often qualitative and only available in narrative form. This project brings together Volterra Consulting, an economic consultancy dealing with practical business issues and Andrew Roach of the University of Glasgow, a historian with expertise in the analysis of networks from his work on medieval heresy and the early Inquisition. It is envisaged that Roach will provide training for Volterra staff in the efficient extraction of information from documents with a view to increasing both the quantity and quality of their modelling data, and participate in Volterra's work in providing practical solutions to business problems.

This project has come about as a result of Roach's collaboration with Paul Ormerod, director of Volterra. Three years ago they published an article in the journal 'Physica A' suggesting that not only did the medieval Cathar heresy display the characteristics of a scale-free network, but that contemporary inquisitors recognised its main characteristics and tailored their strategy accordingly. (A scale-free network consists of a few very well connected hubs amid a number of less connected nodes; it has several distinctive features, notably no 'threshold effect'- the threshold is zero, great robustness against random attack, but vulnerability to assaults which target the vital hubs). The KTF would allow them to develop their collaboration to look at contemporary issues as well as further historical projects.

The KTF would envisage a number of projects based on Volterra's future client base and giving papers to conferences in both the private and public sector. One of Roach and Ormerod's common interests is in reconstructing the networks which influence quite intimate aspects of people's lives, such as the choice of a family doctor, financial adviser or religious allegiance. In all these cases, faced with a bewildering range of 'products' the judging of which would require technical knowledge unavailable to the majority, most people fall back on the recommendations of friends and relations or their own reaction to the professionals involved. A premium seems to be attached to communication skills, availability for consultation, particularly at times of crisis and a general perception of good standing within the community. Often these figures turn out to be very highly connected 'friends of friends'.

Allied to this is a common interest in security issues centring on the vulnerability of networks. Roach and Ormerod noted some time ago in an article in the 'THES', the similarity between the decentralised structures of medieval heretics such as the Cathars and the very loosely connected terrorist organisations of the twenty first century such as Al-Qaida. Counter-terrorism strategies traditionally centre on the capture of the terrorists themselves. Roach and Ormerod aim to explore more systematically the applicability of investigations against heresy which aimed to gain intelligence about the broader community, concentrating on the 'next layer down', those figures who have both international standing and are well connected locally. They act as conduits or messengers whereby initially alien ideas and personalities become accepted in local communities.

Network modelling can also be used to illuminate purely historical questions and Roach and Ormerod are currently working on models to describe the effect of burning 'martyrs' in Marian England and to assess the appropriateness of disease metaphors in contemporary decsriptions of twelfth century heresy.