The extensive nature of group quality

R. Kenna¹ and B. Berche²

¹  Applied Mathematics Research Centre, Coventry University - Coventry, CV1 5FB, UK, EU
²  Institut Jean Lamour (Laboratoire associé au CNRS UMR 7198.) , CNRS-Nancy Université-UPVM - B.P. 70239, F-54506 Vandœuvre lès Nancy Cedex, France, EU

Corresponding author: r.kenna@coventry.ac.uk

Received: 29 March 2010
Accepted: 4 June 2010

Abstract

We consider groups of interacting nodes engaged in an activity as many-body, complex systems and analyse their cooperative behaviour from a mean-field point of view. We show that inter-nodal interactions rather than accumulated individual node strengths dominate the quality of group activity, and give rise to phenomena akin to phase transitions, where the extensive relationship between group quality and quantity reduces. The theory is tested using empirical data on the quantity and quality of scientific research groups, for which critical masses are determined.