A new metric to find the most vulnerable node in complex networks

This paper addresses the problem of finding the most synchrony vulnerable node in complex networks, i.e. the node which removal has the maximum influence on synchronizability of the network. In large-scale networks, brute search techniques are often not computationally cost effective in identifying the most vulnerable node(s). Here, considering the eigenratio of the Laplacian matrix of a graph as the synchronizability metric, we propose a measure in order to approximately rank nodes based on their impact on the synchronizability. This metric is cost effective since it needs a single eigen-decomposition of the Laplacian matrix of the connection graph. Simulation results show that the proposed metric is accurate enough in predicting the most vulnerable node in synthetic networks with scale-free, Watts-Strogatz and Erdos-Rényi structures.