A Hadamard walk model and its application in identification of important edges in complex networks

A Hadamard coin driven quantum walk (i.e., Hadamard walk) model is proposed to identify the important edges of undirected complex networks. In this proposed model, the importance of an edge is scored through the observed probabilities on a pair of nodes with a common edge, based on which the rankings of all important edges are obtained according to the score of each edge. By considering the robustness index of the complex network as estimation standard, experimental results indicate that the capability of the proposed Hadamard walk model to identify important edges is 4.59%∼20.03% higher than existing algorithms in static complex networks. Moreover, to further establish its utility, the proposed model was deployed in a dynamic complex network involving a typical communication scenario found in unmanned aerial vehicle (UAV) swarms. Specifically, we implemented the proposed model in simulations to select significant UAV nodes in a dynamic network and outcomes indicate that our model outperforms various algorithms in the verification of epidemic dynamics model.