Pining Control Algorithm for Complex Networks
Bingjun Wang, Hui Liu, Jiangnqiao Xu, Jiaqi Liu · 2019
In this paper, we quote the concept of resistance distance for Pinning control, and discuss the relationship between the upper bound of the minimum eigenvalue of the grounded Laplacian Matrix and the resistance distance of the Pinning control for one single node. Our simulation results in various networks like BA network, ER network, NW network etc. show that the ranking of the minimum eigenvalue of the grounded Laplacian Matrix is highly consistent with the ranking of resistance distance, much better than the degree ranking, which provides us another approach to estimate the node for Pinning control. In the case of controlling multiple $(l)$ nodes, we use the iterative algorithm to calculate the grounded Laplacian Matrix for better combination of the controlled nodes, through which the computation of NP-hard problem of controlling l nodes can be greatly reduced, and the effect of the iterative algorithm are presented by simulation calculations in different networks, and the smaller l the better effect.