Second-order centrality correlation in scale-free networks

Scale-free networks in which the degree displays a power-law distribution can be classified into assortative, disassortative, and neutral networks according to their degree–degree correlation. The second-order centrality proposed in a distributed computation manner is quick-calculated and accurate to identify critical nodes. We explore the second-order centrality correlation (SOC) for each type of the scale-free networks. The SOC–SOC correlation in assortative network and neutral network behaves similarly to the degree–degree correlation, while it behaves an apparent difference in disassortative networks. Experiments show that the invulnerability of most of scale-free networks behaves similarly under the node removal ordering by SOC centrality and degree centrality, respectively. The netscience network and the Yeast network behave a little differently because they are native disconnecting networks.