Organizations of rich nodes in complex networks

Hidden regularities of complex networks may be different from the properties they show to us externally. In this paper, organization of rich nodes in real world and model networks are investigated. It is found that in scale-free networks, when the rich level is relatively low, the degree distribution of rich nodes follows a power law. On the transitivity and mixing pattern, the clustering coefficient C and assortativity coefficient r   of rich nodes fluctuate with the increment of rich level ρρ in World Wide Web, while in protein–protein Interaction network, a scaling law can be observed in describing the clustering coefficient C of rich nodes as a function of the rich level and an extremum can be expected in the assortativity of rich nodes at a specified rich level. Furthermore, both positive and negative assortativity coefficient can be observed in different rich levels in the studied real world networks, which dedicates that the rich nodes may be organized different from the networks of their own.