Modeling and analysis of information propagation in networks with implicit links

Traditional network models emphasize explicit links, yet many implicit relationships exist in real networks, such as potential social contacts and indirect cooperation. The implicit relationships significantly influence how information propagates. However, the coupling evolution mechanism of information propagation under the combined action of explicit and implicit links is still unclear. Based on it, this paper introduces a novel network model that integrates two types of heterogeneous links: explicit and implicit, and investigates the coupled dynamics of network structure evolution and information propagation at both macroscopic and microscopic levels. By examining interpersonal relationship networks, we propose a propagation dynamics model that accounts for both explicit and implicit relationships. This model elucidates the evolution of information propagation and the conditions under which an outbreak occurs. Our findings indicate that information initially propagates through the explicit network, but once the infection density surpasses a critical threshold, implicit links become fully activated, leading to widespread information propagation across the entire network and a phase transition in infection density. Both theoretical analysis and simulation experiments confirm that the extent of information propagation is contingent upon the scale of explicit and implicit links, as well as the intensity of information propagation. Furthermore, we validate the model’s reliability by comparing real-world data with simulation results.