Attack vulnerability of complex networks with different initial failure

The cascading failure of complex networks has been given more and more attention recent years. On a network, considering that the initial state and the final state after avalanche could both be seen as dynamic equilibriums, we propose a new cascading model. We investigate the vulnerability of each node on Scale-Free networks and Small-World networks during the process of cascading failures. We find that on Scale-Free networks, not only the highest degree nodes but also some small degree nodes absorb extra load higher than their capacities. It can not be found in Small-World networks. Then we study this character and find that with the initial failure node changes, the small degree abnormal nodes also change. Finally, the numerical simulations are verified by the theoretical analysis.