Impacts of inter-layer correlations on network structures and spreading dynamics

In real multilayer networks, the inter-layer hopping behaviours of individuals are a common phenomenon. Although inter-layer structural correlations are obviously vital for inter-layer hopping behaviours and affect both the topological structure and the spreading dynamics, their role remains relatively unexplored. In this paper, we construct multilayer social networks based on real mobile communication data, where layers are coupled through the hopping behaviours of individuals. Using a null model approach, we analyze the impacts of inter-layer strength correlations on both network structures and spreading dynamics. Our findings reveal that as inter-layer strength correlation increases, the average degree, average strength, and clustering coefficient within each layer decrease, while the assortativity coefficient of the sparser layer increases. Regarding spreading dynamics, the final outbreak size in the sparse layer exhibits a non-monotonic dependence on inter-layer strength correlation, reaching a minimum at the value of the real network. The sparse layer in the real multilayer network demonstrates resistance to large-scale propagation, which can be attributed to the diversity of inter-layer coupling relationships. These results indicate that spreading dynamics in multilayer networks can be modulated by intentionally designing inter-layer structures.