The Statistical Analysis of Top Hubs in Growing Geographical Networks with Optimal Policy.

Many practical networks, such as city networks, road networks and neural networks, usually grow up on basis of topological structures and geographical measures. Big hubs, importance of which have been well known in complex networks, still play crucial roles in growing networks with geographical measures. Therefore, it is very necessary to investigate the underlying mechanisms of statistical features of different top hubs in such networks. Here, we propose a growing network model based on optimal policy in geographical ground. Through the statistics of a great number of geographical networks, we find that the degree and position distributions of top four hubs are diverse between them and closely interrelated with each other, and further gain the relationships between the upper limits of top hubs and the size of networks. Then, the underlying mechanisms are explored. Meanwhile, we are diligent to obtain the corresponding relationships of different spatial distribution areas for different top hubs, and compute their abnormal average degrees at different spatial positions, which show significant differences and imply the advantage of spatial positions and intense competition between top hubs. We hope our results could offer useful inspirations for related practical network studies.