Abstract
How to devise an effective measure to quantify the influence of individuals for seeding strategies in multilayer networks is a challenging and yet inadequately explored research problem. Inspired by the well-known gravity law, we propose a weighted gravity centrality measure that utilizes an individual's neighborhood size and social distance between individuals in multiplex networks to quantify individual influence. Supposing that the superposition of multiple relationships between individuals reduces their social distance, and there exists the attenuation of relationship strength between them, we construct the social distance between individuals in multiplex networks by considering the network path information and edge weights. Compared with two commonly used measures-neighborhood size and degree centrality in weighted multiplex networks, the effectiveness of the weighted gravity centrality measure is justified. Furthermore, we evaluate the performance of the proposed centrality measure with three seeding strategies. By simulations, we find that for each seeding strategy, the proposed centrality measure has a higher influence coverage and faster diffusion acceleration in most networks than the other two methods. In addition, the sensitivity analysis of this measure generally obtains a good performance with a small distance radius in line with social distance in reality.