Studying Organisational Topology with Simple Computational Models

The behaviour of many complex systems is influenced by the underlying network topology. In particular, this applies to social systems in which people or organisational units collaboratively solve problems. Network rewiring processes are one useful tool in understanding the relationship between network topology and behaviour. Here we use the Kawachi network rewiring process, together with three simple simulation models of organisational collaboration, to investigate the network characteristics that influence performance. The simulation models are based on the Assignment Problem, the Kuramoto Model from physics, and a novel model of collaborative problem-solving which involves finding numbers with certain characteristics, the existence of which is guaranteed by Lagrange\'s Theorem. For all three models, performance is best when the underlying organisational network has a low average distance between nodes. In addition, the third model identified long-range connectivity between nodes as an important predictor of performance. The commonly-used clustering coefficient, which is a measure of short-range connectivity, did not affect performance. We would expect that long-range network connectivity would also influence the behaviour of other complex systems displaying global self-synchronization. The paper also demonstrates the utility of simple computational models in studying issues of organisational topology.