A key problem in the study and design of complex systems is the apparent disconnection between the microscopic and the macroscopic. It is not straightforward to identify the local interactions that give rise to an observed global phenomenon, nor is it simple to design a system that will exhibit some desired global property using only local knowledge. Here we propose a methodology that allows for the identification of local interactions that give rise to a desired global property of a network, the degree distribution. Given a set of observable processes acting on a network, we determine the conditions that must satisfied to generate a desired steady-state degree distribution. We thereby provide a simple example for a class of tasks where a system can be designed to self-organize to a given state.
Figure 1: Self-organising network with local rules achieve target degree distributions. Shown is the target degree distribution (circles) and the self-organised degree distributions in agent-based simulations (crosses). Simulations for a network of size \(N = 10^4\) are averaged over 90 runs beginning from three different network configurations.