Structure and dynamics of complex systems

Abstract

A family of navigation algorithms for packet transport in complex networks is introduced. These algorithms use deterministic and probabilistic rules which depend, in different ways, on the degree of the node, packet flow and the temporal properties of packet delivery and distribution. On scale-free networks all our algorithms can handle a larger load than the random walk algorithm. I examined the fluctuation properties of packet traffic on scale-free networks and random graphs using random diffusion and a locally navigated diffusive motion with preferred edges. I found that preferential behaviour in either the topology or in the dynamics leads to the scaling of fluctuations of the number of packets passing nodes and the number of packets flowing along edges, respectively. I showed that the absence of any preference results in the absence of scaling. Broad distributions of the return times at nodes and edges illustrate that the basis of the observed scaling is the cooperative behaviour between groups of nodes or edges. I presented an empirical study of the networks created by users within internet news groups and forums and showed that they organise themselves into scale-free trees. The structure of these trees depends on the topic under discussion; specialist topics have trees with a short shallow structure whereas more universal topics are discussed widely and have a deeper tree structure. The correlation function of activity shows long range correlations connected with the users' daily routines. I presented an analysis of empirical data on the arrival and discharge times at a UK Accident and Emergency (A&E) department. I found that discharges rates vary with the workload and that the distribution of the length of stay has a fat tail. A sand pile model is introduced to show that the A&E department is a driven self-organised system. In my model I used a variable input space to mimic the queuing discipline related to different types of patients presenting to the department.