Compact models for influential nodes identification problem in directed networks

Influential nodes identification problem (INIP) is one of the most important problems in complex networks. Existing methods mainly deal with this problem in undirected networks, while few studies focus on it in directed networks. Moreover, the methods designed for identifying influential nodes in undirected networks do not work for directed networks. Therefore, in this paper, we investigate INIP in directed networks. We first propose a novel metric to assess the influence effect of nodes in directed networks. Then, we formulate a compact model for INIP and prove it to be NP-Complete. Furthermore, we design a novel heuristic algorithm for the proposed model by integrating a 2-opt local search into a greedy framework. The experimental results show that, in most cases, the proposed methods outperform traditional measure-based heuristic methods in terms of accuracy and discrimination.