Information Propagation Model Based on 2-dimensional Simplicial Complexes

As a network structure that reflects group relationships in the real world, simplicial complexes have been widely utilized in network models of spreading dynamics. However, the existing studies have solely taken nodes as the objects of research and neglected the mesoscale research perspective. Here, we propose 2-simplices as the research objects. In particular, we consider the structures formed when two 2-simplices are interconnected: the pointer type and the hourglass type. Then, four types of nodes, namely, isolated, triangular, pointer shaped, and hourglass shaped nodes, are used to generate a heterogeneous network. Describe the spread dynamics of networks via the SIS model. This higher-order description of the spreading is analytically formulated via a microscopic Markov chain approach (MMCA) and simulated via a Monte Carlo (MC) experiment. We explore the influence of different initial infection nodes, propagation rates, and 2-simplex reconstruction probabilities on information spreading. The results suggest that when the transmission rate corresponding to the node type of initial infection increases, the propagation range changes greatly. The spreading probability and reconstruction rate of the four structures increase collectively, resulting in the expansion of the infection scale within the system. Moreover, if the initially infected node is an isolated node, in most cases, it slightly influences the system. Our results are in favor of advancing our understanding of information spreading in 2-simplices.