A cost-effective community-hierarchy-based mutual voting approach for influence maximization in complex networks

Influence maximization seeks to choose influential nodes that can spread influence most widely in complex networks. However, current methods often fail to balance the accuracy of selecting such nodes with computational efficiency. To address this challenge, this article proposes a novel approach called Cost-Effective Community-Hierarchy-Based Mutual Voting for influence maximization in complex networks. First, we develop a method for measuring the importance of different nodes in networks based on an original concept of Dual-Scale Community-Hierarchy Information that synthesizes both hierarchy structural information and community structural information of nodes. The community structural information contained in the nodes is measured by a new notion of Hierarchical-Community Entropy. Second, we develop a method named Cost-Effective Mutual-Influence-based Voting for seed nodes selection. Hereinto, a low-computational-cost mutual voting mechanism and an updating strategy called Lazy Score Updating Strategy are newly constructed for optimizing the selecting of seed nodes. Third, we develop a balance index to evaluate the performance of different methods in striking the tradeoff between time complexity and the accuracy of influential nodes identification. Based on this index, we further propose a balance gap to quantify the distance between each method and the best achievable trade-off. Finally, we demonstrate the effectiveness of the proposed approach in terms of time complexity and spreading capability by comparing the experimental results based on five criteria over 13 public datasets. The extensive experiments show that the proposed approach outperforms 16 state-of-the-art techniques on the balance between time complexity and accuracy of influential nodes identification. Compared with the method that has the second highest mean Balance Index, our approach shows an improvement of up to 9.87 %, with the lowest improvement being 5.09 %, and an average improvement of 7.30 %. Moreover, our method consistently reaches the optimal balance point, as indicated by a mean Balance Gap value of zero across all networks and scenarios.