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Complex network will suffer from the node or edge failures due to attacks, which may even lead to whole network paralysis. However, the existing methods for measuring network invulnerability are not applicable for the complex network with dual edges. Therefore, in this paper, a dual-direction different-weight complex network model is designed by emphasizing dual edges with different weights. First, the double-level local network is constructed for each node in the model, which is integrated into the weighted entropy. In addition to revealing how the primary-level and the secondary-level of the structure in the model affect invulnerability of one node, a subject-based primary-level node invulnerability measure named DNNP-Entropy and a path-based double-level node invulnerability measure named INNS-Entropy are proposed. Then, on the basis of that, a node double-level local structure weighted entropy (NDLSW-Entropy)-based measure is designed to measure the invulnerability of each node. By using the designed measure, a top invulnerability nodes mining algorithm is proposed to mine nodes with top invulnerability performance. Two groups of experiments are designed, top nodes mined by different measures and network invulnerability entropy under different attack strategies are discussed respectively. Compared with three typical measures on average, the proposed measure increases the precision of top invulnerability nodes about 20%, 30%, 28.3%, 25%, and 38.3% for five reality different size dual-direction different-weight complex networks, respectively.

Top Invulnerability Nodes Mining in Dual-Direction Different-Weight Complex Network Based on Node Double-Level Local Structure Weighted Entropy