The key player problem in complex oscillator networks and electric power grids: Resistance centralities identify local vulnerabilities

See allHide authors and affiliations

Science Advances  22 Nov 2019:
Vol. 5, no. 11, eaaw8359
DOI: 10.1126/sciadv.aaw8359


Identifying key players in coupled individual systems is a fundamental problem in network theory. We investigate synchronizable network-coupled dynamical systems such as high-voltage electric power grids and coupled oscillators on complex networks. We define key players as nodes that, once perturbed, generate the largest excursion away from synchrony. A spectral decomposition of the coupling matrix gives an elegant solution to this identification problem. We show that, when the coupling matrix is Laplacian, key players are peripheral in the sense of a centrality measure defined from effective resistance distances. For linearly coupled systems, the ranking is efficiently obtained through a single Laplacian matrix inversion, regardless of the operational synchronous state. The resulting ranking index is termed LRank. When nonlinearities are present, a weighted Laplacian matrix inversion gives another ranking index, WLRank. LRank provides a faithful ranking even for well-developed nonlinearities, corresponding to oscillator angle differences up to approximately Δθ ≲ 40°.

This is an open-access article distributed under the terms of the Creative Commons Attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

View Full Text

Stay Connected to Science Advances