The correlation between independent edge and triangle degrees promote the explosive information spreading

Abstract

In recent years, a novel phenomenon of explosive information spreading has been observed in the simplicial configuration model under the higher-order interactions, where a discontinuous transition exists. The model usually considers that the independent edge degree (i.e., the number of single edges attached to a node excluding those belonging to the triangles) and triangle degree (i.e., the number of triangles connected to a node) are uncorrelated. However, whether these degrees correlation exist in real networks and induce the explosive transition of information spreading at higher-order interactions is not very clear. Based on the real social networks data analysis, we find that the triangle degree increases with the independent edge degree approximatively as a power law, indicating a positive correlation between them. To understand how these correlations affect the spreading dynamics, we use an information-spreading model with higher-order interactions on synthetic networks and control the correlated strength of these degrees. Interestingly, our results reveal that the correlated structure would accelerate the information spreading with a fast-spreading speed. In addition, we uncover that the higher-order interactions will induce a discontinuous transition and that there is a bistable region with healthy and endemic states co-existing. Further, we discover that a highly correlated independent edge and triangle degrees will reduce the spreading threshold, which means the correlated structure promotes explosive information spreading. Finally, we utilize the microscopic Markov chain approach(MMCA) to explain the simulations. Our findings may shed some light on understanding the fast-spreading phenomenon of information in real life.