Using LTI Dynamics to Identify the Influential Nodes in a Network.

Networks are used for modeling numerous technical, social or biological systems. In order to better understand the system dynamics, it is a matter of great interest to identify the most important nodes within the network. For a large set of problems, whether it is the optimal use of available resources, spreading information efficiently or even protection from malicious attacks, the most important node is the most influential spreader, the one that is capable of propagating information in the shortest time to a large portion of the network. Here we propose the Node Imposed Response (NiR), a measure which accurately evaluates node spreading power. It outperforms betweenness, degree, k-shell and h-index centrality in many cases and shows the similar accuracy to dynamics-sensitive centrality. We utilize the system-theoretic approach considering the network as a Linear Time-Invariant system. By observing the system response we can quantify the importance of each node. In addition, our study provides a robust tool set for various protective strategies.