Node Importance in Controlled Complex Networks

Abstract

The problem of node importance in a general controlled complex network is investigated in this brief. An index, ControlRank index, to measure the node importance is presented. The index is relatively intuitive and helps unify various indexes that are effective only in the networks with some particular topology. If all nodes except one are pinned in a network, the importance of the unpinned node is sorted in descending order of degree; even if a node is the most significant node, it does not necessarily belong to the most efficient node set; it is very crucial to have an eye on the information balance as for information dissemination in a network; it is reasonable to rank node importance by sorting the node degrees in a scale-free network. The results and phenomena provide us with a broader and clearer perspective to view node importance in complex networks.