Entanglement is one of the most surprising features of composite quantum systems. Yet, challenges remain in our understanding and quantification of the entanglement. There is no unique degree of entanglement from various measures, as presented by numerous studies on quantifying entanglement. As indicated in this paper, any degree of entanglement for two qubits resulting from a particular measure can be detected in excess of onecorresponding pure state. Evidently, those identical entanglement pure states can be counted as a quantitative condition to be satisfied by other proper measures. The most popular measures of pure states for two qubits are based on the same structure, as indicated in this paper. Then, the algorithm to detect the identical entanglement pure states for two qubits is proposed based on randomness distillation. Eventually, two sets of identical entanglement states are listed for two qubits.

It is still a crucial issue to identify influential nodes effectively in the study of complex networks. As for the existing efficiency centrality (EffC), it cannot be applied to a weighted network. In this paper, a modified efficiency centrality ($\rm{EffC}^{m}$) is proposed by extending EffC into weighted networks. The proposed measure trades off the node degree and global structure in a weighted network. The influence of both the sum of the average degree of nodes in the whole network and the average distance of the network is taken into account. Numerical examples are used to illustrate the efficiency of the proposed method.