Identifying the most influential nodes in spreading process on high-order network

Abstract

Identifying the most influential nodes in spreading on the network is an important step to control the speed and range of spreading, which can be applied to accelerate the spread of beneficial information such as healthy behaviors, innovations and suppress the spread of epidemics, rumors, fake news. Existing researches on identification of influential spreaders are mostly based on low-order complex networks with pairwise interactions. However, interactions between individuals occur not only between pairwise nodes but also in groups of three or more nodes, which introduces more complex mechanism of reinforcement and indirect influence. The high-order networks such as simplicial complexes and hypergraphs, can describe features of interactions that go beyond the limitation of pairwise interactions. Currently, there are relatively few works in identifying the most spreading influential nodes in higher-order networks. Some centralities of nodes such as higher-order degree centrality and eigenvector centrality are proposed, but they mostly consider only the network structure. As for identification of influential spreaders, the spreading influence of a node is closely related to the spreading process. In this paper, we work on identification of influential spreaders on the simplicial complexes by taking both network structure and dynamical process into consideration. Firstly, we quantitatively describe the dynamics of disease spreading on simplicial complexes using the Susceptible-Infected-Recovered microscopic Markov equations. Next, we calculate the probability of nodes being infected in the spreading process with the microscopic Markov equations, which is defined as the spreading centrality (SC) of nodes. This spreading centrality involves both the structure of simplicial complex and the dynamical process on it, and is then used to rank the spreading influence of nodes. Simulation results on two types of synthetic simplicial complexes and four real simplicial complexes show that compared with the existing centralities on high-order networks and the optimal centralities of collective influence and nonbacktracking centrality in simple networks, the proposed spreading centrality can more accurately identify the most influential spreaders in the simplicial complexes. In addition, we find that the probability of nodes being infected is highly positively correlated with its influence, which is because disease preferentially reaches nodes with many contacts, who can in turn infect their many neighbors and become influential spreaders.