Leveraging Minimum Nodes for Optimum Key Player Identification in Complex Networks: A Deep Reinforcement Learning Strategy with Structured Reward Shaping

Abstract

The problem of finding key players in a graph, also known as network dismantling, or network disintegration, aims to find an optimal removal sequence of nodes (edges, substructures) through a certain algorithm, ultimately causing functional indicators such as the largest connected component (GCC) or network pair connectivity in the graph to rapidly decline. As a typical NP-hard problem on graphs, recent methods based on reinforcement learning and graph representation learning have effectively solved such problems. However, existing reinforcement-learning-based key-player-identification algorithms often need to remove too many nodes in order to achieve the optimal effect when removing the remaining network until no connected edges remain. The use of a minimum number of nodes while maintaining or surpassing the performance of existing methods is a worthwhile research problem. To this end, a novel algorithm called MiniKey was proposed to tackle such challenges, which employs a specific deep Q-network architecture for reinforcement learning, a novel reward-shaping mechanism based on network functional indicators, and the graph-embedding technique GraphSage to transform network nodes into latent representations. Additionally, a technique dubbed ‘virtual node technology’ is integrated to grasp the overarching feature representation of the whole network. This innovative algorithm can be effectively trained on small-scale simulated graphs while also being scalable to large-scale real-world networks. Importantly, experiments from both six simulated datasets and six real-world datasets demonstrates that MiniKey can achieve optimal performance, striking a perfect balance between the effectiveness of key node identification and the minimization of the number of nodes that is utilized, which holds potential for real-world applications such as curbing misinformation spread in social networks, optimizing traffic in transportation systems, and identifying key targets in biological networks for targeted interventions.