Abstract
The complicated interaction patterns among heterogeneous individuals have a profound impact on the contagion process in the networks. In recent years, there has been increasing evidence for the emergence of many-body interactions between two or more nodes in a wide range of biological and social networks. To encode these multinode interactions explicitly, the simplicial complex is now a popular alternative to simple networks. Meanwhile, the time-varying network has been acknowledged as a key ingredient of the contagion process. In this paper, we consider the connectivity pattern of networks affected by the homophily effect associated with individual attributes and investigate the impact of homophily-driven group interactions on the contagion process in temporal networks. The simplicial complex modeling framework is adopted to capture stochastic interactions between passively selected nodes in the paradigm of activity-driven networks. We study the evolution of infection and the epidemic threshold of the contagion process by both analytical and numerical methods. Our results on statistical topological properties of instantaneous network may shed light on accurately characterizing the evolution curve of infection. Furthermore, we show the impact of the homophily-driven interaction pattern on the epidemic threshold, which generalizes the existing results on both the paradigmatic activity-driven network and the simplicial activity-driven network.
Highlights
Network modeling plays a critical role in identifying structural properties and analyzing contagion processes on networks, such as the spreading of epidemic and malware, as well as the di usion of news and ideas
We investigate the effect of group interactions involving more than two individuals on the contagion process in the time-varying networks
A new network model that extends the paradigmatic activity-driven model to the framework of simplicial complex networks is presented. e statistical properties of the instantaneous network based on this model are explored and incorporated in characterizing the epidemic spreading process
Summary
Network modeling plays a critical role in identifying structural properties and analyzing contagion processes on networks, such as the spreading of epidemic and malware, as well as the di usion of news and ideas. We propose a new model by developing the classical HMF method to more accurately predict the evolution of the epidemic curve To this end, we explore the topological properties of the instantaneous network generated at each step and obtain the degree distribution and the connection correlations among nodes. To quantitatively characterize the epidemic spreading process, we analyze the degree distribution and the connection correlation for nodes belonging to different classes in the instantaneous network. E second term stems from the fact that an inactive node i in class NAa is connected by an active node in Gt, and as the role of neighbor in the group, node i interacts with other neighbor nodes with certain probabilities. We introduce an evaluation parameter εn to further measure the error between theoretical and simulation results. at is, Complexity εn n
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