The rich-club phenomenon, which provides information about the association between nodes, is a useful method to study the hierarchy structure of networks. In this work, we explore the behavior of rich-club coefficient (RCC) in scale-free networks, and find that the degree-based RCC is a power function of degree centrality with power exponent beta and the betweenness-based RCC is a linear function of betweenness centrality with slope theta. Moreover, we calculate the value of RCC in a BA network by deleting nodes and obtain a general expression for RCC as a function of node sequence. On this ba...
