Three Degrees of Influence Rule-Based Grover Walk Model with Applications in Identifying Significant Nodes of Complex Networks

During a quantum walk on a complex network, the observed results contain extensive redundant information generated by interference effects, which makes it difficult to determine a suitable walk step and find the structural characteristics of the network. A Grover coin driven quantum walk model (GWM) is proposed to identify significant nodes in undirected complex networks by simulating the particle moving on the network. To circumvent the negative effects of the associated redundant information, the proposed GWM adds a self-loop to each node and determines a three-step walk by exploiting the three degrees of influence rule. Experiments on correlation, Kendall coefficient, and robustness were reported to validate the effectiveness of the proposed GWM in identifying significant nodes. Outcomes show strong correlation between results from the susceptible-infected-recovered (SIR) model and our GWM, which signify accurate identification of the significant nodes of complex networks by our model. Furthermore, outcomes in terms of Kendall coefficient between different algorithms (comprising of conventional and quantum algorithms) alongside the proposed GWM further attest that the GWM can capture the structural characteristics of networks, e.g., triadic closure and degree.